F64conv.mz: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64conv.bend as F64conv
Lines 123-127 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64conv.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64conv.bend&start_line=123&end_line=127

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
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

# a double with scale at least Z is normal, so its significand is not zero
# the significand at an abstract exponent-is-zero bit b: instantiated at
# False, the hidden bit 2^52 is never evaluated
def mz(+x: F.F64, +b: Bool, +hb: {Nat.is_eq(SF.efield(x), 0n) == b : Bool}) -> {Nat.is_eq(SF.mant(x), 0n) == Nat.is_eq(Nat.add(SF.frac(x), C.shift(52n, SF.b2n(Bool.not(b)))), 0n) : Bool}:
  Equal.cong(Bool, Bool, t => Nat.is_eq(Nat.add(SF.frac(x), C.shift(52n, SF.b2n(Bool.not(t)))), 0n), Nat.is_eq(SF.efield(x), 0n), b, hb)

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=b2n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=efield
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=frac
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=mant
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=F64