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Proof step 12 from proof min-concat (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ min(i ' + j ' + x) = min(min(i, j), min(max(i, j) ' + x))
Proof step 11:
∀ 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 : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d ' + x ≠ []], [CSIMPSEQ : ⊦ d + x = d ' + x])]]