def crem

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix32.bend:176

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/u32div.bend as UD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G

176def crem(+a: U32, +b: U32, +z: Bool, +hz: {U32.is_zero(b) == z : Bool}, +ez: {Nat.is_eq(SG.u32_val(b), 0n) == z : Bool}) -> {SF.mval(~U32, ~SG.u32_val, F.opt(U32, z, U32.mod(a, b))) == SF.keep(Bool.not(Nat.is_eq(SG.u32_val(b), 0n)), Nat.mod(SG.u32_val(a), SG.u32_val(b))) : Maybe<&2, Nat>}:
177  match z:
178    case False{}:
179      %Equal.sym(Bool, Nat.is_eq(SG.u32_val(b), 0n), False{}, ez) : {SF.mval(~U32, ~SG.u32_val, F.opt(U32, False{}, U32.mod(a, b))) == SF.keep(Bool.not(_), Nat.mod(SG.u32_val(a), SG.u32_val(b))) : Maybe<&2, Nat>}
180      G.some_of(~U32, ~SG.u32_val, False{}, {==}, U32.mod(a, b), Nat.mod(SG.u32_val(a), SG.u32_val(b)), UD.mod_nat(a, b, hz))
181    case True{}:
182      %Equal.sym(Bool, Nat.is_eq(SG.u32_val(b), 0n), True{}, ez) : {SF.mval(~U32, ~SG.u32_val, F.opt(U32, True{}, U32.mod(a, b))) == SF.keep(Bool.not(_), Nat.mod(SG.u32_val(a), SG.u32_val(b))) : Maybe<&2, Nat>}
183      {==}