F64divc.dz: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend as F64divc
Lines 100-104 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend&start_line=100&end_line=104

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

# zero divided by a nonzero finite double
def dz(+s: Bool, +xl: U32, +xh: U32, +yl: U32, +yh: U32, +hc: {Nat.is_eq(SF.efield(F.Bits{xl, xh}), 0n) == True{} : Bool}, +hb: {Nat.is_eq(SF.frac(F.Bits{xl, xh}), 0n) == True{} : Bool}, +hzy: {Bool.and(Nat.is_eq(SF.efield(F.Bits{yl, yh}), 0n), Nat.is_eq(SF.frac(F.Bits{yl, yh}), 0n)) == False{} : Bool}) -> {F.zero(s) == SF.div_fin(F.Bits{xl, xh}, F.Bits{yl, yh}, s) : F.F64}:
  +e1 = Equal.cong(Nat, F.F64, z => SF.round(s, Nat.add(Nat.mul(2n, Nat.div(C.shift(200n, z), SF.mant(F.Bits{yl, yh}))), Nat.min(Nat.mod(C.shift(200n, z), SF.mant(F.Bits{yl, yh})), 1n)), Nat.sub(Nat.add(SF.xexp(F.Bits{xl, xh}), SF.zb()), Nat.add(Nat.add(SF.xexp(F.Bits{yl, yh}), SF.kq()), 1n))), SF.mant(F.Bits{xl, xh}), 0n, mant0(xl, xh, hc, hb))
  +e2 = Equal.cong(Nat, F.F64, z => SF.round(s, Nat.add(Nat.mul(2n, Nat.div(C.shift(200n, 0n), z)), Nat.min(Nat.mod(C.shift(200n, 0n), z), 1n)), Nat.sub(Nat.add(SF.xexp(F.Bits{xl, xh}), SF.zb()), Nat.add(Nat.add(SF.xexp(F.Bits{yl, yh}), SF.kq()), 1n))), SF.mant(F.Bits{yl, yh}), 1n+Nat.sub(SF.mant(F.Bits{yl, yh}), 1n), yp_eq(yl, yh, hzy))
  Equal.trans(F.F64, F.zero(s), SF.zero(s), SF.div_fin(F.Bits{xl, xh}, F.Bits{yl, yh}, s), zero_v(s), Equal.sym(F.F64, SF.div_fin(F.Bits{xl, xh}, F.Bits{yl, yh}, s), SF.zero(s), Equal.trans(F.F64, SF.div_fin(F.Bits{xl, xh}, F.Bits{yl, yh}, s), SF.round(s, Nat.add(Nat.mul(2n, Nat.div(C.shift(200n, 0n), SF.mant(F.Bits{yl, yh}))), Nat.min(Nat.mod(C.shift(200n, 0n), SF.mant(F.Bits{yl, yh})), 1n)), Nat.sub(Nat.add(SF.xexp(F.Bits{xl, xh}), SF.zb()), Nat.add(Nat.add(SF.xexp(F.Bits{yl, yh}), SF.kq()), 1n))), SF.zero(s), e1, e2)))

Uses (29):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.min
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend&name=mant0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend&name=yp_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend&name=zero_v
  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=div_fin
  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=kq
  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/spec/math/f64.bend&name=round
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=xexp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=zb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=F64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=zero