F64divc.dsh3: 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 129-134 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=129&end_line=134

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
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as FR

def dsh3(+s: Bool, +ea: Nat, +fa: WU.U64, +eb: Nat, +fb: WU.U64, +z: Bool) -> {F.div_z(s, ea, fa, eb, fb, z) == SF.pick(F.F64, z, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb)))) : F.F64}:
  match z:
    case True{}:
      Equal.trans(F.F64, F.div_z(s, ea, fa, eb, fb, True{}), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, True{}, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb)))), ion(s, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa))), Equal.sym(F.F64, SF.pick(F.F64, True{}, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb)))), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), FR.pk_t(F.F64, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb))))))
    case False{}:
      Equal.trans(F.F64, F.div_z(s, ea, fa, eb, fb, False{}), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb))), SF.pick(F.F64, False{}, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb)))), dsh4(s, ea, fa, eb, fb, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa))), Equal.sym(F.F64, SF.pick(F.F64, False{}, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb)))), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb))), FR.pk_f(F.F64, SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.nan(), F.inf(s)), SF.pick(F.F64, Bool.and(Nat.is_eq(ea, 0n), X.is_zero(fa)), F.zero(s), F.div_n(s, F.norm_e(ea, fa), F.norm_f(ea, fa), F.norm_e(eb, fb), F.norm_f(eb, fb))))))

Uses (21):
  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.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.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend&name=dsh4
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64divc.bend&name=ion
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&name=pk_f
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend&name=pk_t
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/f64.bend&name=pick
  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=div_n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=div_z
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=inf
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=nan
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=norm_e
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=norm_f
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=is_zero