def eq_of

bend-collections-laws-math@1.0.0.0 · proofs/lib/u32alg.bend:321

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U

321def eq_of(+a: U32, +b: U32, +h: {U32.is_eq(a, b) == True{} : Bool}) -> {a == b : U32}:
322  U.injective(a, b, N.eq_from_is_eq(U32.to_nat(a), U32.to_nat(b), L.subst(Cmp, c => {Cmp.is_eq(c) == True{} : Bool}, U32.cmp(a, b), Nat.cmp(U32.to_nat(a), U32.to_nat(b)), U.u32_cmp(a, b), h)))