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Proof step 5 from proof max-app (previous step)

max(min(i, i0) ' + x2) = max(max(x2), min(i, i0)), ∀ x0, y0. # x0 + # y0 < # (i + []) + # (i0 + x2) → (true → x0 = [] ∨ y0 = [] ∨ max(x0 + y0) = max(max(x0), max(y0))) ⊦ max(max(i, i0), max(max(x2), min(i, i0))) = max(max(i0 ' + x2), i), x2 = []

User applied rule apply induction

And obtained the following new goals

Proof step 4:
⊦ max(i ') = i

Rule argument

[substlist-arg: [x0, y0] → [i0 ', x2]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ x + [] = x], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ # (x + y) = # x + # y], [CSIMPSEQ : ⊦ d + x = d ' + x], [CSIMPSEQ : ⊦ # d ' = 0 +1], [CSIMPSEQ : ⊦ d ' ≠ []], [CSIMPSEQ : ⊦ max(i, j) = j ↔ ¬ j < i], [CSIMPSEQ : ⊦ max(i, max(j, j0)) = max(max(i, j), j0)], [CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ max(i, j) < j0 ↔ i < j0 ∧ j < j0], [CSIMPSEQ : ⊦ j < i → max(j, i) = i], [CSIMPSEQ : ⊦ ¬ i < min(i, j)], [CSIMPSEQ : ⊦ min(i, min(j, j0)) = min(min(i, j), j0)], [CSIMPSEQ : ⊦ min(i, j) = min(j, i)])], [EXTRATERMS : (i0 ', x2)]]