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Proof step 12 from proof orderedle-all (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
m ≤ 1 + # y, n ≤ 1 + # y, ordered≤(a0 ' + y), m ≤ n, (a0 ' + y)[n - 1] < (a ' + a0 ' + y)[m], ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m] ⊦ n = 0, a0 < a

Rule argument

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat