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Proof step 25 from proof orderedle-all (previous step)

m ≠ 0, ordered≤(a0 ' + y), m ≤ m0 + 1, (a0 ' + y)[m0] < (a0 ' + y)[m -1], m ≤ 1 + # y, m0 ≤ # y, ∀ 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 26:
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

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%pred-03: ⊦ n -1 = n - 1; from specification nat