PROOF.un.not_tail: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 476-478 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=476&end_line=478

import Base

# 2 + (2N + 2T) = 2 * K, from 1 + (N + T) = K
def un.not_tail(+nv: Nat, +tv: Nat, -k: Nat, ih: {1n+Nat.add(nv, tv) == k : Nat}) -> {2n+Nat.add(Nat.double(nv), Nat.double(tv)) == Nat.double(k) : Nat}:
  Equal.trans(Nat, 2n+Nat.add(Nat.double(nv), Nat.double(tv)), Nat.double(1n+Nat.add(nv, tv)), Nat.double(k), un.succ_cong(1n+Nat.add(Nat.double(nv), Nat.double(tv)), 1n+Nat.double(Nat.add(nv, tv)), un.succ_cong(Nat.add(Nat.double(nv), Nat.double(tv)), Nat.double(Nat.add(nv, tv)), Equal.sym(Nat, Nat.double(Nat.add(nv, tv)), Nat.add(Nat.double(nv), Nat.double(tv)), un.double_add(nv, tv)))), un.double_cong(1n+Nat.add(nv, tv), k, ih))

Uses (8):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.double_add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.double_cong
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.succ_cong