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Proof step 18 from proof min-concat (previous step)

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

User applied rule apply induction

And obtained the following new goals

Proof step 17:
⊦ min(i ') = i

Rule argument

[substlist-arg: [x0, y0] → [max(i, i0) ', y]]

Additional information

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