ProofBase.le_add.k: def of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_base.bend as ProofBase
Lines 695-705 of minebender-game@1.0.0.0/proof_base.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_base.bend&start_line=695&end_line=705

import Base

def le_add.k(+a: Nat, +b: Nat, +c: Nat, +d: Nat, r1: LeW(a, b), r2: LeW(c, d)) ->
  {Nat.is_le(Nat.add(a, c), Nat.add(b, d)) == True{} : Bool}:
  match r1:
    case (+k1, e1):
      match r2:
        case (+k2, e2):
          %Equal.sym(Nat, b, Nat.add(a, k1), e1) : {Nat.is_le(Nat.add(a, c), Nat.add(_, d)) == True{} : Bool}
          %Equal.sym(Nat, d, Nat.add(c, k2), e2) : {Nat.is_le(Nat.add(a, c), Nat.add(Nat.add(a, k1), _)) == True{} : Bool}
          %Equal.sym(Nat, Nat.add(Nat.add(a, k1), Nat.add(c, k2)), Nat.add(Nat.add(a, c), Nat.add(k1, k2)), add_swap(a, k1, c, k2)) :
            {Nat.is_le(Nat.add(a, c), _) == True{} : Bool}
          le_of_add(Nat.add(a, c), Nat.add(k1, k2))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=LeW
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=add_swap
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=le_of_add