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Proof step 8 from proof min-concat (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ min(i ') = i
Proof step 7:
x2 = [] ∨ min(max(i, i0) ' + x2) = min(min(x2), max(i, i0)), x2 = [] ∨ min(i0 ' + x2) = min(min(x2), i0), ∀ x0, y0. # x0 + # y0 < # (i + []) + # (i0 + x2) → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ min(min(i, i0), min(max(i, i0) ' + x2)) = min(min(i0 ' + x2), i)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ' ≠ []])]]