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Proof step 24 from proof max-concat (previous step)

min(i, i0) < i1, ∀ x0, y0. # x0 + # y0 < # (i + i0 + i1 + x2) + # y → (true → x0 = [] ∨ y0 = [] ∨ max(x0 + y0) = max(max(x0), max(y0))) ⊦ y = [], max(i1, max(max(min(i, i0) ' + x2 + y), max(i, i0))) = max(i1, max(max(min(i, i0) ' + x2), max(max(y), max(i, i0))))

User applied rule apply induction

And obtained the following new goals

Proof step 23:
min(i, i0) ' = [] ∨ x2 = [] ∨ max(min(i, i0) ' + x2) = max(max(min(i, i0) '), max(x2)), min(i, i0) < i1, ∀ x0, y0. # x0 + # y0 < # (i + i0 + i1 + x2) + # y → (true → x0 = [] ∨ y0 = [] ∨ max(x0 + y0) = max(max(x0), max(y0))) ⊦ y = [], max(i1, max(max(min(i, i0) ' + x2 + y), max(i, i0))) = max(i1, max(max(min(i, i0) ' + x2), max(max(y), max(i, i0))))

Rule argument

[substlist-arg: [x0, y0] → [min(i, i0) ', x2]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # d ' = 0 +1], [CSIMPSEQ : ⊦ d + x = d ' + x], [CSIMPSEQ : ⊦ # (x + y) = # x + # y], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : n < n0 ⊦ ((* n)) ≠ m0 + ((* n0))], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (min(i, i0) ', x2)]]