def dm_fin

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/u32div.bend:180

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

180def dm_fin(+aw: Word(32n), +b: U32, qr: Word(32n) & U32, h: inv(32n, aw, v(b), qr)) -> {Nat.add(Nat.mul(v(U32.div.fin(qr)), v(b)), v(U32.mod.fin(qr))) == v(U32{aw}) : Nat} & {Nat.is_lt(v(U32.mod.fin(qr)), v(b)) == True{} : Bool}:
181  match qr:
182    case (+q, +r):
183      (he, hr) = h
184      +eq = Equal.trans(Nat, Nat.add(Nat.mul(v(U32{q}), v(b)), v(r)), Nat.add(Nat.mul(S.unsigned(32n, q), v(b)), v(r)), v(U32{aw}),
185        Equal.cong(Nat, Nat, z => Nat.add(Nat.mul(z, v(b)), v(r)), v(U32{q}), S.unsigned(32n, q), vw(q)),
186        Equal.trans(Nat, Nat.add(Nat.mul(S.unsigned(32n, q), v(b)), v(r)), S.unsigned(32n, aw), v(U32{aw}), he, Equal.sym(Nat, v(U32{aw}), S.unsigned(32n, aw), vw(aw))))
187      (eq, hr)