def nzc

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64next.bend:339

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/proofs/math/typed/f64bits.bend as FB
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64cmp.bend as FC

339def nzc(+x: F.F64, +y: F.F64, +hu: {Bool.or(SF.is_nan(x), SF.is_nan(y)) == False{} : Bool}, +iz: Bool, +hiz: {SF.is_zero(x) == iz : Bool}) -> {F.na_z(x, y, iz) == SF.pick(F.F64, iz, SF.encode(SF.sign(y), 0n, 1n), STEP(x, y)) : F.F64}:
340  match iz:
341    case True{}:
342      nz0(y)
343    case False{}:
344      +e1 = Equal.cong(Bool, F.F64, t => F.na_step(x, Bool.xor(t, F.signbit(x))), F.lt(x, y), Cmp.is_lt(SF.ord(x, y)), ltc(x, y, hu))
345      +e2 = Equal.cong(Bool, F.F64, t => F.na_step(x, Bool.xor(Cmp.is_lt(SF.ord(x, y)), t)), F.signbit(x), SF.sign(x), FB.signbit_value(x))
346      +e3 = st_c(x, FC.or_l(SF.is_nan(x), SF.is_nan(y), hu), hiz, Bool.xor(Cmp.is_lt(SF.ord(x, y)), SF.sign(x)))
347      +a1 = F.na_step(x, Bool.xor(Cmp.is_lt(SF.ord(x, y)), F.signbit(x)))
348      +a2 = F.na_step(x, Bool.xor(Cmp.is_lt(SF.ord(x, y)), SF.sign(x)))
349      Equal.trans(F.F64, F.na_step(x, Bool.xor(F.lt(x, y), F.signbit(x))), a1, STEP(x, y), e1, Equal.trans(F.F64, a1, a2, STEP(x, y), e2, e3))