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

x1 = i0 + x, ∀ x0, y0. # x0 + # y0 < # (i + x1) + # y → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ y = [], min((i ' + x1) + y) = min(min(y), min(i ' + x1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
⊦ min(i ' + j ' + x) = min(min(i, j), min(max(i, j) ' + x))
Proof step 23:
∀ x0, y0. # x0 + # y0 < # (i + i0 + x) + # y → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ y = [], min(min(i, i0), min(max(i, i0) ' + x + y)) = min(min(min(i, i0), min(max(i, i0) ' + x)), min(y))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d + x = d ' + x])]]