ProofGen.le_trans.k: def of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 836-845 of minebender-game@1.0.0.0/proof_gen.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_gen.bend&start_line=836&end_line=845

import Base
import minebender-game@1.0.0.0/proof_base.bend as P

def le_trans.k(+a: Nat, +b: Nat, +c: Nat, r1: P.LeW(a, b), r2: P.LeW(b, c)) -> {Nat.is_le(a, c) == True{} : Bool}:
  match r1:
    case (+k1, e1):
      match r2:
        case (+k2, e2):
          %Equal.sym(Nat, c, Nat.add(b, k2), e2) : {Nat.is_le(a, _) == True{} : Bool}
          %Equal.sym(Nat, b, Nat.add(a, k1), e1) : {Nat.is_le(a, Nat.add(_, k2)) == True{} : Bool}
          %Equal.sym(Nat, Nat.add(Nat.add(a, k1), k2), Nat.add(a, Nat.add(k1, k2)), P.add_assoc(a, k1, k2)) :
            {Nat.is_le(a, _) == True{} : Bool}
          P.le_of_add(a, 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_assoc
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=le_of_add