def icd

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64close.bend:38

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/f64addv.bend as AV

38def icd(+a: F.F64, +b: F.F64, +rel: F.F64, +at: F.F64) -> {F.ic_d(a, b, rel, at, F.abs(F.sub(b, a))) == SF.ic_near(a, b, rel, at, D(a, b)) : Bool}:
39  +d = D(a, b)
40  +e0 = Equal.cong(F.F64, Bool, t => F.ic_d(a, b, rel, at, t), F.abs(F.sub(b, a)), d, fabs_v(F.sub(b, a), SF.add(b, SF.neg(a)), AV.sub_value(b, a)))
41  Equal.trans(Bool, F.ic_d(a, b, rel, at, F.abs(F.sub(b, a))), F.ic_d(a, b, rel, at, d), SF.ic_near(a, b, rel, at, d), e0, icd_t(a, b, rel, at, d))