F64sqc.ssh2: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqc.bend as F64sqc
Lines 283-288 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqc.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqc.bend&start_line=283&end_line=288

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

def ssh2(+x: F.F64, +s: Bool, +e: Nat, +f: WU.U64, +z: Bool) -> {F.sq_sign(x, s, e, f, z) == SF.pick(F.F64, z, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n)))) : F.F64}:
  match z:
    case True{}:
      Equal.trans(F.F64, F.sq_sign(x, s, e, f, True{}), x, SF.pick(F.F64, True{}, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n)))), {==}, Equal.sym(F.F64, SF.pick(F.F64, True{}, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n)))), x, FR.pk_t(F.F64, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n))))))
    case False{}:
      Equal.trans(F.F64, F.sq_sign(x, s, e, f, False{}), SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n))), SF.pick(F.F64, False{}, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n)))), ssh3(e, f, s), Equal.sym(F.F64, SF.pick(F.F64, False{}, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n)))), SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n))), FR.pk_f(F.F64, x, SF.pick(F.F64, s, F.nan(), F.sq_n(F.norm_e(e, f), F.norm_f(e, f), Nat.is_eq(Nat.mod(F.norm_e(e, f), 2n), 1n))))))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=Nat.mod
  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/proofs/math/typed/f64sqc.bend&name=ssh3
  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=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=sq_n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/f64.bend&name=sq_sign
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64