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Proof step 26 from proof orderedle-all (previous step)

m ≤ 1 + # y, m0 ≤ # y, ordered≤(a0 ' + y), m ≤ m0 + 1, (a0 ' + y)[m0] < (a0 ' + y)[m - 1], ∀ m1, n. m1 ≤ n ∧ ¬ # y < n → ¬ (a0 ' + y)[n] < (a0 ' + y)[m1] ⊦ m = 0, a0 < a

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
m = m2 + 1, m ≤ 1 + # y, m0 ≤ # y, ordered≤(a0 ' + y), m ≤ m0 + 1, (a0 ' + y)[m0] < (a0 ' + y)[m2], ∀ m1, n. m1 ≤ n ∧ ¬ # y < n → ¬ (a0 ' + y)[n] < (a0 ' + y)[m1] ⊦ m = 0, a0 < a

Rule argument

spec: nat inst: name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m2] flags:

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m2