Ineq.le_mul2: 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 47-49 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=47&end_line=49

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

# a <= c, b <= d: a b <= c d
def le_mul2(+a: Nat, +b: Nat, +c: Nat, +d: Nat, +h1: {Nat.is_le(a, c) == True{} : Bool}, +h2: {Nat.is_le(b, d) == True{} : Bool}) -> {Nat.is_le(Nat.mul(a, b), Nat.mul(c, d)) == True{} : Bool}:
  N.le_trans(Nat.mul(a, b), Nat.mul(c, b), Nat.mul(c, d), AR.mul_le(a, c, b, h1), le_mul_r(c, b, d, h2))

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=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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=le_mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&name=mul_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans