def csub

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:102

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/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
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/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G

102def csub(+a: WU.U64, +b: WU.U64, +ok: Bool, +hok: {Nat.is_le(SG.u64_val(b), SG.u64_val(a)) == ok : Bool}) -> {SF.mval(~WU.U64, ~SG.u64_val, F.opt(WU.U64, X.lt(a, b), X.sub(a, b))) == SF.keep(ok, Nat.sub(SG.u64_val(a), SG.u64_val(b))) : Maybe<&2, Nat>}:
103  match ok:
104    case True{}:
105      G.some_of(~WU.U64, ~SG.u64_val, X.lt(a, b), Equal.trans(Bool, X.lt(a, b), Nat.is_lt(SG.u64_val(a), SG.u64_val(b)), False{}, WA.lt_value(a, b), N.le_not_lt(SG.u64_val(a), SG.u64_val(b), hok)), X.sub(a, b), Nat.sub(SG.u64_val(a), SG.u64_val(b)), WA.sub_value(a, b, hok))
106    case False{}:
107      G.none_of(~WU.U64, ~SG.u64_val, X.lt(a, b), Equal.trans(Bool, X.lt(a, b), Nat.is_lt(SG.u64_val(a), SG.u64_val(b)), True{}, WA.lt_value(a, b), N.not_le_lt(SG.u64_val(b), SG.u64_val(a), hok)), X.sub(a, b))