PROOF.AP.alg2: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 242-245 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=242&end_line=245

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def AP.alg2(+r: Nat, +y: Nat) -> {Nat.double(Nat.add(r, 1n+y)) == Nat.add(1n+Nat.double(r), 1n+Nat.double(y)) : Nat}:
  %Equal.sym(Nat, Nat.add(r, 1n+y), 1n+Nat.add(r, y), UL.nat_add_succ(r, y)) : {Nat.double(_) == Nat.add(1n+Nat.double(r), 1n+Nat.double(y)) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.double(r), 1n+Nat.double(y)), 1n+Nat.add(Nat.double(r), Nat.double(y)), UL.nat_add_succ(Nat.double(r), Nat.double(y))) : {Nat.double(1n+Nat.add(r, y)) == 1n+_ : Nat}
  AP.succ_cong(1n+Nat.double(Nat.add(r, y)), 1n+Nat.add(Nat.double(r), Nat.double(y)), AP.succ_cong(Nat.double(Nat.add(r, y)), Nat.add(Nat.double(r), Nat.double(y)), AP.double_add(r, y)))

Uses (7):
  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.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.double_add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ