[
  "\u0013�\u0011��\t#.�8\tב{��",
  [
    [
      "Lib.NatMod.mk_nat_comm_monoid",
      1,
      2,
      1,
      [ "@query" ],
      0,
      "e0018e425cc2ec5bcd3c55de5faa83a5"
    ],
    [
      "Lib.NatMod.pow",
      1,
      2,
      1,
      [
        "@MaxIFuel_assumption", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_ae567c2fb75be05905677af440075565_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_1", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "well-founded-ordering-on-nat"
      ],
      0,
      "5c1d220150c15301750cd142314de0e1"
    ],
    [
      "Lib.NatMod.lemma_pow0",
      1,
      2,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "equation_Prims.nat",
        "equation_with_fuel_Lib.NatMod.pow.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Equality",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2"
      ],
      0,
      "648609648f3b493a53c1c467c42c44f2"
    ],
    [
      "Lib.NatMod.lemma_pow1",
      1,
      2,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "equation_Prims.nat",
        "equation_with_fuel_Lib.NatMod.pow.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Multiply", "primitive_Prims.op_Subtraction",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "typing_Lib.NatMod.pow"
      ],
      0,
      "dfe55a5439bbc6934e1083dd032da25b"
    ],
    [
      "Lib.NatMod.lemma_pow_unfold",
      1,
      2,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "73b818a05fbba6b11df2d7257e5ed7f9"
    ],
    [
      "Lib.NatMod.lemma_pow_unfold",
      2,
      2,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow.fuel_instrumented",
        "@fuel_irrelevance_Lib.NatMod.pow.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "equation_Prims.nat", "equation_Prims.pos",
        "equation_with_fuel_Lib.NatMod.pow.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Subtraction",
        "projection_inverse_BoxBool_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "40ba22e845c0320f6ced814683b93b1f"
    ],
    [
      "Lib.NatMod.lemma_pow_gt_zero",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_1",
        "binder_x_f26957a7e62b271a8736230b1e9c83c1_0", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals", "equation_Prims.pos",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Multiply", "primitive_Prims.op_Subtraction",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "well-founded-ordering-on-nat"
      ],
      0,
      "765b2afe2a495f8497479334563e6dc4"
    ],
    [
      "Lib.NatMod.lemma_pow_ge_zero",
      1,
      0,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_1", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals", "equation_Prims.pos",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "lemma_Lib.NatMod.lemma_pow_gt_zero",
        "primitive_Prims.op_Equality", "primitive_Prims.op_Multiply",
        "primitive_Prims.op_Subtraction",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "well-founded-ordering-on-nat"
      ],
      0,
      "e8fec876590bdbb5f6584d46280d43cc"
    ],
    [
      "Lib.NatMod.lemma_pow_nat_is_pow",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_ae567c2fb75be05905677af440075565_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_1",
        "equation_Lib.Exponentiation.mul", "equation_Lib.Exponentiation.one",
        "equation_Lib.NatMod.mk_nat_comm_monoid", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing",
        "interpretation_Tm_abs_767452e6211eb45132bb0ad477208a19",
        "interpretation_Tm_abs_bdd1351fbdaffcab615fdbdd8ed277ef",
        "primitive_Prims.op_Equality", "primitive_Prims.op_Subtraction",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_mul",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_one",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_mul",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_one",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "token_correspondence_Lib.Exponentiation.mul",
        "token_correspondence_Lib.Exponentiation.one",
        "token_correspondence_Prims.op_Multiply",
        "well-founded-ordering-on-nat"
      ],
      0,
      "d4929252408c6fe861c4004df809e9a9"
    ],
    [
      "Lib.NatMod.lemma_pow_one",
      1,
      0,
      0,
      [
        "@query", "equation_Lib.Exponentiation.one",
        "equation_Lib.NatMod.mk_nat_comm_monoid",
        "interpretation_Tm_abs_bdd1351fbdaffcab615fdbdd8ed277ef",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_one",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_one",
        "token_correspondence_Lib.Exponentiation.one"
      ],
      0,
      "1f464548f470eba1ccd3946490728f59"
    ],
    [
      "Lib.NatMod.lemma_pow_add",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.nat",
        "primitive_Prims.op_Addition", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2"
      ],
      0,
      "faf025a57066b809f9faa47f11035ee7"
    ],
    [
      "Lib.NatMod.lemma_pow_add",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.Exponentiation.mul",
        "equation_Lib.NatMod.mk_nat_comm_monoid", "equation_Prims.nat",
        "interpretation_Tm_abs_767452e6211eb45132bb0ad477208a19",
        "primitive_Prims.op_Addition",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_mul",
        "projection_inverse_BoxInt_proj_0",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_mul",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "token_correspondence_Lib.Exponentiation.mul",
        "token_correspondence_Prims.op_Multiply"
      ],
      0,
      "9cf5134aed4afc758c4d038f6d6481b9"
    ],
    [
      "Lib.NatMod.lemma_pow_mul",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.nat",
        "primitive_Prims.op_Multiply", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2"
      ],
      0,
      "48acc29e7f13aa511c66b4f6bcddba32"
    ],
    [
      "Lib.NatMod.lemma_pow_mul",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.nat",
        "primitive_Prims.op_Multiply", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2"
      ],
      0,
      "389039409b109450a354a547a21d750d"
    ],
    [
      "Lib.NatMod.lemma_pow_double",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.nat",
        "primitive_Prims.op_Addition", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2"
      ],
      0,
      "3439f301a6fcd0876450849bf602a7ac"
    ],
    [
      "Lib.NatMod.lemma_pow_double",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.Exponentiation.mul",
        "equation_Lib.NatMod.mk_nat_comm_monoid", "equation_Prims.nat",
        "int_inversion",
        "interpretation_Tm_abs_767452e6211eb45132bb0ad477208a19",
        "primitive_Prims.op_Addition",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_mul",
        "projection_inverse_BoxInt_proj_0",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_mul",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "token_correspondence_Lib.Exponentiation.mul",
        "token_correspondence_Prims.op_Multiply"
      ],
      0,
      "2637765e4a96b944ae60aea112534d61"
    ],
    [
      "Lib.NatMod.lemma_pow_mul_base",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.Exponentiation.mul",
        "equation_Lib.NatMod.mk_nat_comm_monoid", "int_inversion",
        "interpretation_Tm_abs_767452e6211eb45132bb0ad477208a19",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_mul",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_mul",
        "token_correspondence_Lib.Exponentiation.mul",
        "token_correspondence_Prims.op_Multiply"
      ],
      0,
      "c602c0c4e1e0b7b4a2fe6db9e2dce0a0"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_base",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "096633149f1c7993fa9a9f1e38119719"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_base",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_f9f88af3b1e2dbc99e38f49301940025"
      ],
      0,
      "6df963bab676eabc72c44b56c2960b02"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_base",
      3,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_ae567c2fb75be05905677af440075565_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_1",
        "binder_x_f26957a7e62b271a8736230b1e9c83c1_2", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals", "equation_Prims.pos",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Subtraction",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "well-founded-ordering-on-nat"
      ],
      0,
      "b718532f987e07275585e747596bc35e"
    ],
    [
      "Lib.NatMod.one_mod",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "int_inversion", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "66bac7992b125b42144594b9ef03fa0d"
    ],
    [
      "Lib.NatMod.mul_mod",
      1,
      2,
      1,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "int_inversion", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "5a879c4d56ab2c67ae735caec921f5b7"
    ],
    [
      "Lib.NatMod.add_mod",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "int_inversion", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "28342732fbcb6090d7ab493b0658bdf6"
    ],
    [
      "Lib.NatMod.sub_mod",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "int_inversion", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "237c4188152eeccc923ed42fc7ba98aa"
    ],
    [
      "Lib.NatMod.lemma_mul_mod_one",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.mul_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Lib.NatMod.one_mod",
        "equation_Prims.nat", "equation_Prims.pos", "int_inversion",
        "primitive_Prims.op_Modulus", "primitive_Prims.op_Multiply",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "typing_Lib.NatMod.mul_mod", "typing_Lib.NatMod.one_mod"
      ],
      0,
      "8ba7a85208ba81f4af6dadd4fbbdcf1f"
    ],
    [
      "Lib.NatMod.lemma_mul_mod_assoc",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.mul_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Prims.nat",
        "equation_Prims.pos", "int_inversion",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c"
      ],
      0,
      "06d3a30ec0c83903f6c5d4d92780f9e0"
    ],
    [
      "Lib.NatMod.lemma_mul_mod_comm",
      1,
      0,
      0,
      [
        "@query", "equation_Lib.NatMod.mul_mod",
        "primitive_Prims.op_Multiply"
      ],
      0,
      "713b0d797a6fdb1835e8ba3ce1edd2b0"
    ],
    [
      "Lib.NatMod.pow_mod_",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_03a5d00a837dd83ad22cac00d90eeef8_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_2", "equation_Prims.nat",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Division",
        "primitive_Prims.op_Equality", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_4fe9a5df27ca5859eef8add9fc6819fb",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "well-founded-ordering-on-nat"
      ],
      0,
      "4008fea5c8253b818cc4dfb9b54d245a"
    ],
    [
      "Lib.NatMod.lemma_pow_mod0",
      1,
      2,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow_mod_.fuel_instrumented",
        "@query", "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "equation_Lib.NatMod.pow_mod", "equation_Prims.nat",
        "equation_with_fuel_Lib.NatMod.pow_mod_.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__", "int_typing",
        "primitive_Prims.op_Equality",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2"
      ],
      0,
      "6f66150d2e5d6b2381fdc687fed7a6e9"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_unfold0",
      1,
      2,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "primitive_Prims.op_Division", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_2e4eb0dfc8e927c366ec35a49feaf594",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "bb6d6b4c00a060db27742aa39f25cb69"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_unfold0",
      2,
      2,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow_mod_.fuel_instrumented",
        "@fuel_irrelevance_Lib.NatMod.pow_mod_.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "equation_Lib.NatMod.pow_mod", "equation_Prims.nat",
        "equation_Prims.pos",
        "equation_with_fuel_Lib.NatMod.pow_mod_.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "primitive_Prims.op_Division",
        "primitive_Prims.op_Equality", "projection_inverse_BoxBool_proj_0",
        "refinement_interpretation_Tm_refine_2e4eb0dfc8e927c366ec35a49feaf594",
        "refinement_interpretation_Tm_refine_4fe9a5df27ca5859eef8add9fc6819fb",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "473a84a3edd400fb44a82470ba7a8962"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_unfold1",
      1,
      2,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "primitive_Prims.op_Division", "primitive_Prims.op_Modulus",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_951246198cead7debc9ffd1c9af03d7b"
      ],
      0,
      "0cc275d89860209c4ee7092dd09c717a"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_unfold1",
      2,
      2,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_Lib.NatMod.pow_mod_.fuel_instrumented",
        "@fuel_irrelevance_Lib.NatMod.pow_mod_.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "equation_Lib.NatMod.pow_mod", "equation_Prims.nat",
        "equation_Prims.pos",
        "equation_with_fuel_Lib.NatMod.pow_mod_.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "primitive_Prims.op_Division",
        "primitive_Prims.op_Equality", "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_4fe9a5df27ca5859eef8add9fc6819fb",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_951246198cead7debc9ffd1c9af03d7b"
      ],
      0,
      "7c37f799168bbf8d37953d2916b9f405"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "8303156a4848fddc75633971920ed8b5"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_6092045e3746216d4a7e28a7890a43dd",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "825b8b138e781011cac5d095b0f1f0c6"
    ],
    [
      "Lib.NatMod.lemma_pow_mod_",
      3,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_03a5d00a837dd83ad22cac00d90eeef8_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_2",
        "binder_x_cbdc2d3d67eb1d9b86cdf331a98a2d14_1",
        "equation_Lib.NatMod.mul_mod", "equation_Lib.NatMod.nat_mod",
        "equation_Prims.nat", "equation_Prims.pos",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Addition",
        "primitive_Prims.op_Division", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Modulus", "primitive_Prims.op_Multiply",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_4fe9a5df27ca5859eef8add9fc6819fb",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "unit_inversion", "unit_typing", "well-founded-ordering-on-nat"
      ],
      0,
      "bd970ae2023daca25f3bf8705d9c7b99"
    ],
    [
      "Lib.NatMod.lemma_pow_mod",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "50d76bd1499588d43c3f014dfae753f5"
    ],
    [
      "Lib.NatMod.lemma_pow_mod",
      2,
      0,
      0,
      [ "@query" ],
      0,
      "1046a541b5f06364f004ed60b56b5fda"
    ],
    [
      "Lib.NatMod.lemma_pow_nat_mod_is_pow",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "2f0d1151326f3b0d3656ddf8a0cb769d"
    ],
    [
      "Lib.NatMod.lemma_pow_nat_mod_is_pow",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_9940fd5216d1969f95f956276466686b"
      ],
      0,
      "6e0d7842fd843c17dafadddcd90e983b"
    ],
    [
      "Lib.NatMod.lemma_pow_nat_mod_is_pow",
      3,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_03a5d00a837dd83ad22cac00d90eeef8_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_2",
        "binder_x_cbdc2d3d67eb1d9b86cdf331a98a2d14_1",
        "equation_Lib.Exponentiation.mul", "equation_Lib.Exponentiation.one",
        "equation_Lib.NatMod.mk_nat_mod_comm_monoid",
        "equation_Lib.NatMod.mul_mod", "equation_Lib.NatMod.nat_mod",
        "equation_Lib.NatMod.one_mod", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals", "equation_Prims.pos",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing",
        "interpretation_Tm_abs_767452e6211eb45132bb0ad477208a19",
        "interpretation_Tm_abs_bdd1351fbdaffcab615fdbdd8ed277ef",
        "primitive_Prims.op_Equality", "primitive_Prims.op_Subtraction",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_mul",
        "proj_equation_Lib.Exponentiation.Mkcomm_monoid_one",
        "projection_inverse_BoxBool_proj_0",
        "projection_inverse_BoxInt_proj_0",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_mul",
        "projection_inverse_Lib.Exponentiation.Mkcomm_monoid_one",
        "refinement_interpretation_Tm_refine_4fe9a5df27ca5859eef8add9fc6819fb",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "token_correspondence_Lib.Exponentiation.__proj__Mkcomm_monoid__item__mul",
        "token_correspondence_Lib.Exponentiation.mul",
        "token_correspondence_Lib.Exponentiation.one",
        "token_correspondence_Lib.NatMod.mul_mod",
        "well-founded-ordering-on-nat"
      ],
      0,
      "376e77179ddbb9c18c1cec7cbedb87ed"
    ],
    [
      "Lib.NatMod.lemma_add_mod_one",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Prims.pos",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5"
      ],
      0,
      "0ee4066a9764304ee8fc2388402347fa"
    ],
    [
      "Lib.NatMod.lemma_add_mod_one",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.add_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Prims.nat",
        "equation_Prims.pos", "int_inversion", "primitive_Prims.op_Addition",
        "primitive_Prims.op_Modulus", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c"
      ],
      0,
      "47d441f27a97cce78dd2bbc4094ef4ef"
    ],
    [
      "Lib.NatMod.lemma_add_mod_assoc",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.add_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Prims.nat",
        "equation_Prims.pos", "int_inversion", "primitive_Prims.op_Addition",
        "primitive_Prims.op_Modulus", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c"
      ],
      0,
      "60f51ae96991b690d119db2e0d79de68"
    ],
    [
      "Lib.NatMod.lemma_add_mod_comm",
      1,
      0,
      0,
      [
        "@query", "equation_Lib.NatMod.add_mod",
        "primitive_Prims.op_Addition"
      ],
      0,
      "30e377d59f3fd85dae7664e4a193793a"
    ],
    [
      "Lib.NatMod.lemma_mod_distributivity_add_right",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.add_mod",
        "equation_Lib.NatMod.mul_mod", "equation_Lib.NatMod.nat_mod",
        "equation_Prims.nat", "equation_Prims.pos", "int_inversion",
        "primitive_Prims.op_Modulus", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "typing_Lib.NatMod.add_mod", "typing_Lib.NatMod.mul_mod"
      ],
      0,
      "e3f66f7758d84146f40ce6c3c09dcab3"
    ],
    [
      "Lib.NatMod.lemma_mod_distributivity_add_left",
      1,
      0,
      0,
      [
        "@query", "equation_Lib.NatMod.add_mod",
        "equation_Lib.NatMod.mul_mod", "primitive_Prims.op_Multiply"
      ],
      0,
      "c4d79e259fa87ab4606f55128251d61e"
    ],
    [
      "Lib.NatMod.lemma_mod_distributivity_sub_right",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.mul_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Lib.NatMod.sub_mod",
        "equation_Prims.nat", "equation_Prims.pos", "int_inversion",
        "primitive_Prims.op_Addition", "primitive_Prims.op_Minus",
        "primitive_Prims.op_Modulus", "primitive_Prims.op_Multiply",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "typing_Lib.NatMod.mul_mod", "typing_Lib.NatMod.sub_mod"
      ],
      0,
      "8032366e0c5f9d20a7d790216743a8b5"
    ],
    [
      "Lib.NatMod.lemma_mod_distributivity_sub_left",
      1,
      0,
      0,
      [
        "@query", "equation_Lib.NatMod.mul_mod",
        "equation_Lib.NatMod.sub_mod", "primitive_Prims.op_Multiply"
      ],
      0,
      "8bf3521ff76a6e5a689e5c809c623d8d"
    ],
    [
      "Lib.NatMod.inv_mod",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.prime",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "db3bc281f8d6b2005197def278517e99"
    ],
    [
      "Lib.NatMod.lemma_inv_mod_both",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.inv_mod",
        "equation_Lib.NatMod.mul_mod", "equation_Lib.NatMod.nat_mod",
        "equation_Lib.NatMod.prime", "equation_Prims.nat",
        "equation_Prims.pos", "int_inversion", "primitive_Prims.op_Modulus",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "ed2db478459b7418bb75bab495a09fab"
    ],
    [
      "Lib.NatMod.pow_eq",
      1,
      1,
      0,
      [
        "@MaxFuel_assumption", "@MaxIFuel_assumption",
        "@fuel_correspondence_FStar.Math.Fermat.pow.fuel_instrumented",
        "@fuel_correspondence_Lib.NatMod.pow.fuel_instrumented",
        "@fuel_irrelevance_FStar.Math.Fermat.pow.fuel_instrumented",
        "@fuel_irrelevance_Lib.NatMod.pow.fuel_instrumented", "@query",
        "Prims_pretyping_ae567c2fb75be05905677af440075565",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_0",
        "binder_x_bb4e1c9af0265270f8e7a5f250f730e2_1", "equation_Prims.nat",
        "equation_Prims.op_Equals_Equals_Equals",
        "equation_with_fuel_FStar.Math.Fermat.pow.fuel_instrumented",
        "equation_with_fuel_Lib.NatMod.pow.fuel_instrumented",
        "function_token_typing_Prims.__cache_version_number__",
        "int_inversion", "int_typing", "primitive_Prims.op_Equality",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "well-founded-ordering-on-nat"
      ],
      0,
      "2669f16e70d05ae8140904a1c92a18b2"
    ],
    [
      "Lib.NatMod.lemma_div_mod_prime",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.div_mod",
        "equation_Lib.NatMod.inv_mod", "equation_Lib.NatMod.mul_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Lib.NatMod.prime",
        "equation_Prims.pos", "int_inversion", "int_typing",
        "primitive_Prims.op_Addition", "primitive_Prims.op_Multiply",
        "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_828958215008c7ce6253d89a707fd615",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "3736aa14419b48f1623220729f1a140d"
    ],
    [
      "Lib.NatMod.lemma_div_mod_prime_one",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.prime",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "9c8166f0dfee2b6111793daf70a0a2b2"
    ],
    [
      "Lib.NatMod.lemma_div_mod_prime_one",
      2,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.div_mod",
        "equation_Lib.NatMod.inv_mod", "equation_Lib.NatMod.mul_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Lib.NatMod.prime",
        "equation_Prims.nat", "int_inversion", "primitive_Prims.op_Modulus",
        "primitive_Prims.op_Multiply", "primitive_Prims.op_Subtraction",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "db048d6778aab57b78ccd0a8bb1c8d05"
    ],
    [
      "Lib.NatMod.lemma_div_mod_prime_cancel",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.div_mod",
        "equation_Lib.NatMod.mul_mod", "equation_Lib.NatMod.nat_mod",
        "equation_Lib.NatMod.prime", "equation_Prims.nat",
        "equation_Prims.pos", "int_inversion", "int_typing",
        "primitive_Prims.op_Modulus", "primitive_Prims.op_Multiply",
        "projection_inverse_BoxInt_proj_0",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_828958215008c7ce6253d89a707fd615",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "bed9a9fdca04785a5af91cea8260e251"
    ],
    [
      "Lib.NatMod.lemma_div_mod_prime_to_one_denominator",
      1,
      0,
      0,
      [
        "@MaxIFuel_assumption", "@query", "equation_Lib.NatMod.div_mod",
        "equation_Lib.NatMod.nat_mod", "equation_Lib.NatMod.prime",
        "equation_Prims.nat", "equation_Prims.pos", "int_inversion",
        "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2",
        "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5",
        "refinement_interpretation_Tm_refine_828958215008c7ce6253d89a707fd615",
        "refinement_interpretation_Tm_refine_c1424615841f28cac7fc34e92b7ff33c",
        "refinement_interpretation_Tm_refine_c94e6d54c545297365221a2bcc484b9a"
      ],
      0,
      "8d9d6d508149aa1410228cc38d9d58a2"
    ]
  ]
]