Ineq.lt_of_le_lt: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as Ineq
Lines 73-75 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&start_line=73&end_line=75

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

# x < b and b <= c: x < c, and friends with rewriting
def lt_of_le_lt(+a: Nat, +b: Nat, +c: Nat, +h1: {Nat.is_le(a, b) == True{} : Bool}, +h2: {Nat.is_lt(b, c) == True{} : Bool}) -> {Nat.is_lt(a, c) == True{} : Bool}:
  N.le_lt_trans(a, b, c, h1, h2)

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_lt_trans