def lt_pred

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:236

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/logic.bend as L

236def lt_pred(+base: Nat, +p: Nat, +n: Nat, +h: {Nat.is_lt(Nat.add(base, 1n+p), n) == True{} : Bool}) -> {Nat.is_lt(Nat.add(base, p), n) == True{} : Bool}:
237  N.lt_trans(Nat.add(base, p), Nat.add(base, 1n+p), n, L.subst(Nat, z => {Nat.is_lt(Nat.add(base, p), z) == True{} : Bool}, 1n+Nat.add(base, p), Nat.add(base, 1n+p), Equal.sym(Nat, Nat.add(base, 1n+p), 1n+Nat.add(base, p), N.add_succ(base, p)), N.lt_succ(Nat.add(base, p))), h)