def le_sub

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/memory.bend:403

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

403def le_sub(+base: Nat, +k: Nat, +n: Nat, +h: {Nat.is_le(Nat.add(base, k), n) == True{} : Bool}) -> {Nat.is_le(k, Nat.sub(n, base)) == True{} : Bool}:
404  match base n:
405    case 0n _:
406      L.subst(Nat, z => {Nat.is_le(k, z) == True{} : Bool}, n, Nat.sub(n, 0n), Equal.sym(Nat, Nat.sub(n, 0n), n, N.sub_zero(n)), h)
407    case 1n+b 0n:
408      Empty.absurd({Nat.is_le(k, Nat.sub(0n, 1n+b)) == True{} : Bool}, L.false_true(h))
409    case 1n+ +b 1n+ +m:
410      le_sub(b, k, m, h)