[ "»êW»(\u0018\u007fÿæ+êBʱð‰", [ [ "Vale.Math.Lemmas.Int.multiply_fractions", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "e16d4f58b8864c4d4be204449ac7235d" ], [ "Vale.Math.Lemmas.Int.multiply_fractions", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "71a2663ad7b7c958e3247f4f91678978" ], [ "Vale.Math.Lemmas.Int.lemma_div_mod", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "ecbfa9f5cab9057ece9e4a427819f5cd" ], [ "Vale.Math.Lemmas.Int.lemma_div_mod", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "int_inversion", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "1e8f6e4be3747e4c956864dae7f99f53" ], [ "Vale.Math.Lemmas.Int.lemma_div_lt", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "b2t_def", "equation_Prims.l_and", "equation_Prims.squash", "l_and-interp", "primitive_Prims.op_LessThanOrEqual", "projection_inverse_BoxBool_proj_0", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_2de20c066034c13bf76e9c0b94f4806c" ], 0, "494f34ec4386ef3333eef5a11feb320f" ], [ "Vale.Math.Lemmas.Int.lemma_div_lt", 2, 0, 0, [ "@MaxIFuel_assumption", "@fuel_correspondence_Prims.pow2.fuel_instrumented", "@query", "equation_Prims.nat", "equation_Prims.pos", "int_inversion", "int_typing", "primitive_Prims.op_GreaterThanOrEqual", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5", "typing_Prims.pow2" ], 0, "6f49ecbd95f743dab7e9ff1e968ee179" ], [ "Vale.Math.Lemmas.Int.bounded_multiple_is_zero", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "int_inversion" ], 0, "237d1c1f6850dd29e853a8bd329a26dc" ], [ "Vale.Math.Lemmas.Int.small_div", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "f78d8d85182d6dc15463f3b68f7aef25" ], [ "Vale.Math.Lemmas.Int.small_div", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.nat", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "74419785fb1a71a707fafa90e325ae69" ], [ "Vale.Math.Lemmas.Int.small_mod", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "084252ca7fc823a4682fdde3a01168c5" ], [ "Vale.Math.Lemmas.Int.small_mod", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.nat", "equation_Prims.pos", "int_inversion", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "20285e9fb3e357707784ff961519c0b4" ], [ "Vale.Math.Lemmas.Int.lt_multiple_is_equal", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.nat", "int_inversion", "int_typing", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2" ], 0, "d16f1bf22f8ecd80cabcb9dc51150c80" ], [ "Vale.Math.Lemmas.Int.add_div_mod_1", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "3572e426da0d84cbe45aa6a3c925c089" ], [ "Vale.Math.Lemmas.Int.sub_div_mod_1", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "a1f1ace57959d9e99eaef8d0bc649d76" ], [ "Vale.Math.Lemmas.Int.lemma_div_mod_plus", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5", "refinement_interpretation_Tm_refine_ac5cb6e21e2ee5b82fa6ef28ee8fe0c5" ], 0, "2aa47685c5a3370ea5374855330602ec" ], [ "Vale.Math.Lemmas.Int.lemma_div_mod_plus", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "Prims_pretyping_ae567c2fb75be05905677af440075565", "binder_x_ae567c2fb75be05905677af440075565_1", "binder_x_f26957a7e62b271a8736230b1e9c83c1_2", "equality_tok_Prims.LexTop@tok", "equation_Prims.pos", "function_token_typing_Prims.__cache_version_number__", "int_inversion", "int_typing", "primitive_Prims.op_Equality", "primitive_Prims.op_GreaterThan", "projection_inverse_BoxBool_proj_0", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5", "unit_inversion", "unit_typing", "well-founded-ordering-on-nat" ], 0, "a7069ceade269f10a9cd922f0bc70c4a" ], [ "Vale.Math.Lemmas.Int.lemma_div_plus", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "2ec51caf2949374cd61c07d45ad535c8" ], [ "Vale.Math.Lemmas.Int.lemma_div_plus", 2, 0, 0, [ "@query" ], 0, "0ed757efc2e96d5721a73e6cf1a764f6" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "7132d0f00668a81321347c301d1e93f7" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus", 2, 0, 0, [ "@query" ], 0, "417dc943f090fbcd42e3b0e52dadda0b" ], [ "Vale.Math.Lemmas.Int.cancel_mul_div", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "294703d891c8509b8701200796576d50" ], [ "Vale.Math.Lemmas.Int.cancel_mul_div", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "int_inversion", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "862cc2bf760510128f702763a354e553" ], [ "Vale.Math.Lemmas.Int.cancel_mul_mod", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "e33ad7d4fedaf9c22bd24c6f541ae21b" ], [ "Vale.Math.Lemmas.Int.cancel_mul_mod", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "399b18f573d8e61a99c9d737c53d0a50" ], [ "Vale.Math.Lemmas.Int.mod_add_both", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "cb1b6ad1f60edf1e8960a4756d1368ab" ], [ "Vale.Math.Lemmas.Int.mod_add_both", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "0fd0c9b5f53d540c5db1973a3361d850" ], [ "Vale.Math.Lemmas.Int.lemma_mod_add_distr", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "bfdedac5831135f77e7aa990a697c50d" ], [ "Vale.Math.Lemmas.Int.lemma_mod_add_distr", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "ee78eec97487880f3531ebe5a232989e" ], [ "Vale.Math.Lemmas.Int.lemma_mod_sub_distr", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "894b0696753d6637995a2cdf37486c3d" ], [ "Vale.Math.Lemmas.Int.lemma_mod_sub_distr", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "85420e177a4a1c7267e9ee83543c102a" ], [ "Vale.Math.Lemmas.Int.lemma_mod_mul_distr_l", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "63e261643b30e9819791b2d5e3f8e576" ], [ "Vale.Math.Lemmas.Int.lemma_mod_mul_distr_l", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_462196ad07942fe00cf7b5fd6567777a", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "cb1a5f2a6890aa38a7f9f2d1869e2898" ], [ "Vale.Math.Lemmas.Int.lemma_mod_mul_distr_l", 3, 0, 0, [ "@MaxIFuel_assumption", "@query", "Prims_pretyping_ae567c2fb75be05905677af440075565", "binder_x_ae567c2fb75be05905677af440075565_1", "binder_x_f26957a7e62b271a8736230b1e9c83c1_2", "equality_tok_Prims.LexTop@tok", "equation_Prims.pos", "function_token_typing_Prims.__cache_version_number__", "int_inversion", "int_typing", "primitive_Prims.op_Equality", "primitive_Prims.op_GreaterThan", "primitive_Prims.op_GreaterThanOrEqual", "projection_inverse_BoxBool_proj_0", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5", "unit_inversion", "unit_typing", "well-founded-ordering-on-nat" ], 0, "90e865e135febddd6ad9dbd0afb1dddb" ], [ "Vale.Math.Lemmas.Int.lemma_mod_mul_distr_r", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "9d74f331825042215144fff54dcb6e02" ], [ "Vale.Math.Lemmas.Int.lemma_mod_mul_distr_r", 2, 0, 0, [ "@query" ], 0, "cef441ff36e79b40deb3ee74712b9849" ], [ "Vale.Math.Lemmas.Int.lemma_div_exact", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "a64ffa4c3907b5a024ac3e3e660f5d36" ], [ "Vale.Math.Lemmas.Int.lemma_div_exact", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "int_inversion", "projection_inverse_BoxInt_proj_0" ], 0, "582ba9430640933be280ac86e1504cd9" ], [ "Vale.Math.Lemmas.Int.div_exact_r", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "5a319f4fbed5dfb5eeb1e2978c195365" ], [ "Vale.Math.Lemmas.Int.div_exact_r", 2, 0, 0, [ "@query" ], 0, "fdb9931dc637a0efa370a84cda6ba2b3" ], [ "Vale.Math.Lemmas.Int.lemma_mod_spec", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "ee779ccbee1db98e0073044a29b3ebe2" ], [ "Vale.Math.Lemmas.Int.lemma_mod_spec", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "b13e9b85ad7ea97dbe44913c5440d24e" ], [ "Vale.Math.Lemmas.Int.lemma_mod_spec2", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "a2b6e91c3fd2729add29b614548e55f8" ], [ "Vale.Math.Lemmas.Int.lemma_mod_spec2", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "int_inversion", "projection_inverse_BoxInt_proj_0" ], 0, "e616cff32f18de5d8ae1c2a89b0b7b4e" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus_distr_l", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "5697a02082533a46f1ea8e3ff4cfdb89" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus_distr_l", 2, 0, 0, [ "@query" ], 0, "5b145e14978501d8db392da3f1bb41f9" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus_distr_r", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "6c8aa19a7e8b376ab1f9baf087608528" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus_distr_r", 2, 0, 0, [ "@query" ], 0, "f805e315da8902e077048bcfdb9e6c73" ], [ "Vale.Math.Lemmas.Int.small_division_lemma_2", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "764d615f507a11d27cde9b22039460c0" ], [ "Vale.Math.Lemmas.Int.small_division_lemma_2", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "9d18eb06a9983bf68c61a8b79dbb03cb" ], [ "Vale.Math.Lemmas.Int.multiplication_order_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "8bce70597c7141c7606fd76076d8bf55" ], [ "Vale.Math.Lemmas.Int.division_propriety", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "297b94f9cbc1e010013321008bb6add4" ], [ "Vale.Math.Lemmas.Int.division_propriety", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "46c2ba3c88e21b33a3b68bd8f97a6ced" ], [ "Vale.Math.Lemmas.Int.division_definition", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "aaab81021882a64707343fc995f11fa7" ], [ "Vale.Math.Lemmas.Int.division_definition", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "int_inversion", "projection_inverse_BoxInt_proj_0" ], 0, "d20d56f3d16e2a8a6dae2f67237b4f5b" ], [ "Vale.Math.Lemmas.Int.multiple_division_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "490615b8f5eed35bb26b95e6eead4d54" ], [ "Vale.Math.Lemmas.Int.multiple_division_lemma", 2, 0, 0, [ "@query" ], 0, "c4dfdaacd1ddd1a2fdd19328adcb1fc5" ], [ "Vale.Math.Lemmas.Int.multiple_modulo_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "b3ac9e6b971950d983ae77e2477430fc" ], [ "Vale.Math.Lemmas.Int.multiple_modulo_lemma", 2, 0, 0, [ "@query" ], 0, "1ebf56f181b64236c5a333a6e6116c96" ], [ "Vale.Math.Lemmas.Int.division_addition_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "a434e818092dfb551031ab2229e974d6" ], [ "Vale.Math.Lemmas.Int.division_sub_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "ab00526e3da1b18d45829c967e4f30b4" ], [ "Vale.Math.Lemmas.Int.division_sub_lemma", 2, 0, 0, [ "@query" ], 0, "9d82f2ccaee8a866ff8190a845043eaa" ], [ "Vale.Math.Lemmas.Int.modulo_distributivity", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "8d1dd3e0a1ba0646df5e1ed217f7c5c5" ], [ "Vale.Math.Lemmas.Int.modulo_distributivity", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "18c0da1e5f732c92b13841d6e52b8a4e" ], [ "Vale.Math.Lemmas.Int.modulo_addition_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "a243c194f514c7116205da458b8d045e" ], [ "Vale.Math.Lemmas.Int.lemma_mod_sub", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "7cfaa5bed715bd7a4337804d6fd2ecb0" ], [ "Vale.Math.Lemmas.Int.lemma_mod_sub", 2, 0, 0, [ "@query" ], 0, "5febf4865ffe600481cf854d0c728fb8" ], [ "Vale.Math.Lemmas.Int.mod_mult_exact", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "fc852b104130f41431230f62d733d234" ], [ "Vale.Math.Lemmas.Int.mod_mult_exact", 2, 0, 0, [ "@query", "projection_inverse_BoxInt_proj_0" ], 0, "e9923539062f571d7e3ea35bbb5c5ee5" ], [ "Vale.Math.Lemmas.Int.mod_mul_div_exact", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "eq2-interp", "equation_Prims.pos", "equation_Prims.squash", "refinement_interpretation_Tm_refine_2de20c066034c13bf76e9c0b94f4806c", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "66ec9af0196c192ff66fd4da35a870de" ], [ "Vale.Math.Lemmas.Int.mod_mul_div_exact", 2, 0, 0, [ "@query", "projection_inverse_BoxInt_proj_0" ], 0, "3eb2467a69c74fc74f540b05b00dee16" ], [ "Vale.Math.Lemmas.Int.mod_pow2_div2", 1, 1, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "71cbcc4678050a6bfdb71b0cad8ea8a3" ], [ "Vale.Math.Lemmas.Int.mod_pow2_div2", 2, 1, 0, [ "@MaxFuel_assumption", "@MaxIFuel_assumption", "@fuel_correspondence_Prims.pow2.fuel_instrumented", "@fuel_irrelevance_Prims.pow2.fuel_instrumented", "@query", "equation_Prims.nat", "equation_Prims.pos", "equation_with_fuel_Prims.pow2.fuel_instrumented", "int_inversion", "primitive_Prims.op_Multiply", "primitive_Prims.op_Subtraction", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_542f9d4f129664613f2483a6c88bc7c2", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "8a8115c765d92f80010a390572edb970" ], [ "Vale.Math.Lemmas.Int.division_multiplication_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "4cd32dd97e997aa6814f802416e47522" ], [ "Vale.Math.Lemmas.Int.division_multiplication_lemma", 2, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "projection_inverse_BoxInt_proj_0", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "2c0949ff5eb3421622aa6c935c5e1342" ], [ "Vale.Math.Lemmas.Int.modulo_modulo_lemma", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.pos", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "972b7a73705b1aba84b7893cc6891788" ], [ "Vale.Math.Lemmas.Int.modulo_modulo_lemma", 2, 0, 0, [ "@query", "projection_inverse_BoxInt_proj_0" ], 0, "ba7f9cbcbd47127f4da0d189558586af" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus_injective", 1, 0, 0, [ "@MaxIFuel_assumption", "@query", "equation_Prims.eqtype", "equation_Prims.nat", "equation_Prims.pos", "function_token_typing_Prims.int", "haseqTm_refine_542f9d4f129664613f2483a6c88bc7c2", "refinement_interpretation_Tm_refine_414d0a9f578ab0048252f8c8f552b99f", "refinement_interpretation_Tm_refine_774ba3f728d91ead8ef40be66c9802e5" ], 0, "6601c8b89eb7f23ac2a0839d661380ff" ], [ "Vale.Math.Lemmas.Int.lemma_mod_plus_injective", 2, 0, 0, [ "@query" ], 0, "f611eea0b183db493a2fb59a9d4b6dc0" ] ] ]