def from_nat_word

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/u32.bend:85

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

85def from_nat_word(+i: Nat, +k: Nat, +hk: {Nat.is_le(k, 32n) == True{} : Bool}, +h: {Nat.is_lt(i, SC.pow2(k)) == True{} : Bool}) -> {U32.from_nat(i) == U32{S.from_nat(32n, i)} : U32}:
86  match i:
87    case 0n:
88      {==}
89    case 1n+p:
90      +hp = N.lt_trans(p, 1n+p, SC.pow2(k), N.lt_succ(p), h)
91      from_nat_step(p, S.from_nat(32n, p), S.from_nat(32n, 1n+p), from_nat_word(p, k, hk, hp), inc_from(32n, p, from_nat_value_k(32n, k, p, hk, hp)))