def le_sc

bend-collections-laws-math@1.0.0.0 · proofs/lib/arith.bend:57

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

57def le_sc(+k: Nat, +x: Nat) -> {Nat.is_le(x, sc(k, x)) == True{} : Bool}:
58  match k:
59    case 0n:
60      N.le_refl(x)
61    case 1n+j:
62      N.le_trans(x, sc(j, x), Nat.double(sc(j, x)), le_sc(j, x), N.double_self_le(sc(j, x)))