def na_c

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64next.bend:359

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

359def na_c(+x: F.F64, +y: F.F64, +u: Bool, +hu: {Bool.or(SF.is_nan(x), SF.is_nan(y)) == u : Bool}) -> {F.na_nan(x, y, u) == SF.pick(F.F64, Bool.not(Bool.not(u)), SF.qnan(), SF.pick(F.F64, Cmp.is_eq(SF.ord(x, y)), y, SF.pick(F.F64, SF.is_zero(x), SF.encode(SF.sign(y), 0n, 1n), STEP(x, y)))) : F.F64}:
360  match u:
361    case True{}:
362      {==}
363    case False{}:
364      +R = SF.pick(F.F64, Cmp.is_eq(SF.ord(x, y)), y, SF.pick(F.F64, SF.is_zero(x), SF.encode(SF.sign(y), 0n, 1n), STEP(x, y)))
365      +e1 = Equal.cong(Bool, F.F64, t => F.na_eq(x, y, t), F.eq(x, y), Cmp.is_eq(SF.ord(x, y)), eqc(x, y, hu))
366      Equal.trans(F.F64, F.na_eq(x, y, F.eq(x, y)), F.na_eq(x, y, Cmp.is_eq(SF.ord(x, y))), R, e1, neq_c(x, y, hu, Cmp.is_eq(SF.ord(x, y))))