def iinf

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64close.bend:50

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

50def iinf(+a: F.F64, +b: F.F64, +rel: F.F64, +at: F.F64, +big: Bool) -> {F.ic_inf(a, b, rel, at, big) == SF.pick(Bool, big, False{}, SF.ic_near(a, b, rel, at, D(a, b))) : Bool}:
51  match big:
52    case True{}:
53      {==}
54    case False{}:
55      +u = F.ic_d(a, b, rel, at, F.abs(F.sub(b, a)))
56      +n = SF.ic_near(a, b, rel, at, D(a, b))
57      Equal.trans(Bool, F.ic_inf(a, b, rel, at, False{}), u, SF.pick(Bool, False{}, False{}, n), ii_f(a, b, rel, at), Equal.trans(Bool, u, n, SF.pick(Bool, False{}, False{}, n), icd(a, b, rel, at), Equal.sym(Bool, SF.pick(Bool, False{}, False{}, n), n, pk_f(False{}, n))))