Fix32.ssub: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend as Fix32
Lines 131-136 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&start_line=131&end_line=136

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/src/math/fixed.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

def ssub(+a: U32, +b: U32, +c: Bool, +hn: {Nat.is_lt(SG.u32_val(a), SG.u32_val(b)) == c : Bool}) -> {SG.u32_val(F.pick(U32, c, 0, U32.sub(a, b))) == Nat.sub(SG.u32_val(a), SG.u32_val(b)) : Nat}:
  match c:
    case True{}:
      Equal.sym(Nat, Nat.sub(SG.u32_val(a), SG.u32_val(b)), 0n, sub_big(SG.u32_val(a), SG.u32_val(b), N.lt_le(SG.u32_val(a), SG.u32_val(b), hn)))
    case False{}:
      sub_exact(a, b, N.not_lt_le(SG.u32_val(a), SG.u32_val(b), hn))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=not_lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&name=sub_big
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&name=sub_exact
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/generic.bend&name=u32_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/fixed.bend&name=pick