def lt_iff_c

bend-collections-laws-math@1.0.0.0 · proofs/math/number/fixprime.bend:129

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

129def lt_iff_c(+a: Nat, +b: Nat, +c: Bool, +hc: {Nat.is_lt(a, b) == c : Bool}) -> {c == Nat.is_le(1n+a, b) : Bool}:
130  match c:
131    case True{}:
132      Equal.sym(Bool, Nat.is_le(1n+a, b), True{}, N.lt_succ_le_succ(a, b, hc))
133    case False{}:
134      le_c(a, b, Nat.is_le(1n+a, b), {==}, hc)