def lts

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64cmp.bend:235

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X

235def lts(+xl: U32, +xh: U32, +yl: U32, +yh: U32, +sa: Bool, +sb: Bool, +mc: Cmp, +h: {X.lt(F.mag(F.Bits{xl, xh}), F.mag(F.Bits{yl, yh})) == Cmp.is_lt(mc) : Bool}, +h2: {X.lt(F.mag(F.Bits{yl, yh}), F.mag(F.Bits{xl, xh})) == Cmp.is_lt(SF.flip(mc)) : Bool}) -> {F.lt_s(F.Bits{xl, xh}, F.Bits{yl, yh}, sa, sb) == Cmp.is_lt(SF.pick(Cmp, Bool.not(Bool.xor(sa, sb)), SF.pick(Cmp, sa, SF.flip(mc), mc), SF.pick(Cmp, sa, LT{}, GT{}))) : Bool}:
236  match sa sb:
237    case True{} False{}:
238      {==}
239    case False{} True{}:
240      {==}
241    case False{} False{}:
242      h
243    case True{} True{}:
244      h2