def dmant_value

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64tools.bend:71

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/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64light.bend as FL

71def dmant_value(+x: F.F64) -> {SW.value(F.dmant(x)) == SF.mant(x) : Nat}:
72  match x:
73    case F.Bits{+xl, +xh}:
74      +e1 = Equal.cong(Nat, Nat, t => SW.value(F.dmant_z(F.frac(F.Bits{xl, xh}), Nat.is_eq(t, 0n))), F.exp_field(F.Bits{xl, xh}), SF.efield(F.Bits{xl, xh}), FL.hea(xl, xh))
75      Equal.trans(Nat, SW.value(F.dmant(F.Bits{xl, xh})), SW.value(F.dmant_z(F.frac(F.Bits{xl, xh}), Nat.is_eq(SF.efield(F.Bits{xl, xh}), 0n))), SF.mant(F.Bits{xl, xh}), e1, dm(1n, {==}, F.frac(F.Bits{xl, xh}), SF.frac(F.Bits{xl, xh}), FL.hfr(xl, xh), FL.hF(xl, xh), Nat.is_eq(SF.efield(F.Bits{xl, xh}), 0n)))