Fixprime.lt_iff_c: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend as Fixprime
Lines 129-134 of bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&start_line=129&end_line=134

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

def 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}:
  match c:
    case True{}:
      Equal.sym(Bool, Nat.is_le(1n+a, b), True{}, N.lt_succ_le_succ(a, b, hc))
    case False{}:
      le_c(a, b, Nat.is_le(1n+a, b), {==}, hc)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_succ_le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=le_c