SignedPROOF.le_add: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend as SignedPROOF
Lines 263-271 of bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&start_line=263&end_line=271

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/signed.bend as Signed

# The inference classifies the exact sizes' product against the count
# (Signed.capped) instead of forming it. These lemmas give capped as the
# classification of exact_product, so the laws stated with exact_product hold.
def le_add(+a: Nat, +b: Nat) -> {Nat.is_le(a, Nat.add(a, b)) == True{} : Bool}:
  match a:
    case 0n:
      Arith.le_zero(b)
    case 1n+p:
      le_add(p, b)

Uses (5):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=le_zero