def csub

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix32.bend:112

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/fixed.bend as F
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/math/typed/fixgen.bend as G

112def csub(+a: U32, +b: U32, +ok: Bool, +hok: {Nat.is_le(SG.u32_val(b), SG.u32_val(a)) == ok : Bool}) -> {SF.mval(~U32, ~SG.u32_val, F.opt(U32, U32.is_lt(a, b), U32.sub(a, b))) == SF.keep(ok, Nat.sub(SG.u32_val(a), SG.u32_val(b))) : Maybe<&2, Nat>}:
113  match ok:
114    case True{}:
115      G.some_of(~U32, ~SG.u32_val, U32.is_lt(a, b), Equal.trans(Bool, U32.is_lt(a, b), Nat.is_lt(SG.u32_val(a), SG.u32_val(b)), False{}, lt_nat(a, b), N.le_not_lt(SG.u32_val(a), SG.u32_val(b), hok)), U32.sub(a, b), Nat.sub(SG.u32_val(a), SG.u32_val(b)), sub_exact(a, b, hok))
116    case False{}:
117      G.none_of(~U32, ~SG.u32_val, U32.is_lt(a, b), Equal.trans(Bool, U32.is_lt(a, b), Nat.is_lt(SG.u32_val(a), SG.u32_val(b)), True{}, lt_nat(a, b), N.not_le_lt(SG.u32_val(b), SG.u32_val(a), hok)), U32.sub(a, b))