Arith.le_sc: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as Arith
Lines 57-62 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&start_line=57&end_line=62

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

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

Uses (8):
  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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=double_self_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans