QueueProof.key_succ.premise: def of bend-kit-scheduler@0.4.1.0
Import: import bend-kit-scheduler@0.4.1.0/queue_proof.bend as QueueProof
Lines 51-52 of bend-kit-scheduler@0.4.1.0/queue_proof.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-scheduler@0.4.1.0/queue_proof.bend&start_line=51&end_line=52

import Base
import bend-kit-scheduler@0.4.1.0/queue.bend as Q

def key_succ.premise(+d: Nat, +e: Nat, +i: Nat, +j: Nat, +b: Bool, p: {Q.le.same(Nat.is_eq(d, e), i, j, 1n+d, 1n+e) == b : Bool}) -> {Q.le.same(Nat.is_eq(d, e), i, j, d, e) == b : Bool}:
  Equal.trans(Bool, Q.le.same(Nat.is_eq(d, e), i, j, d, e), Q.le.same(Nat.is_eq(d, e), i, j, 1n+d, 1n+e), b, Equal.sym(Bool, Q.le.same(Nat.is_eq(d, e), i, j, 1n+d, 1n+e), Q.le.same(Nat.is_eq(d, e), i, j, d, e), key_succ(Nat.is_eq(d, e), i, j, d, e)), p)

Uses (7):
  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=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-kit-scheduler@0.4.1.0/queue.bend&name=le.same
  https://jend.leeeet.dev/definition.txt?path=bend-kit-scheduler@0.4.1.0/queue_proof.bend&name=key_succ