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Proof step 12 from proof less-same (previous step)

n < # x0, ∀ n0, a1. n0 + 1 < # x0 → less#(a1, x0[n0, x0[n0 + 1]][n0 + 1, x0[n0]]) = less#(a1, x0) ⊦ less#(a, (a0 ' + x0)[n, x0[n]][n + 1, x0[n - 1]]) = (a0 < a ⊃ 1;0) + less#(a, x0), n = 0, x0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
n = m + 1, n < # x0, ∀ n0, a1. n0 + 1 < # x0 → less#(a1, x0[n0, x0[n0 + 1]][n0 + 1, x0[n0]]) = less#(a1, x0) ⊦ less#(a, (a0 ' + x0)[n, x0[n]][n + 1, x0[m]]) = (a0 < a ⊃ 1;0) + less#(a, x0), n = 0, x0 = []

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m