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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i0 ≤ i, ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(i0, min(i ' + x)) = i, min(i0, min(i ' + x)) = i0, min(i0, min(i ' + x)) ∈ x

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ min(i, j) = min(j, i)], [CSIMPSEQ : ⊦ min(i, min(j, j0)) = min(min(i, j), j0)], [CSIMPSEQ : ⊦ ¬ j < i → min(j, i) = i], [CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ max(i, max(j, j0)) = max(max(i, j), j0)], [CSIMPSEQ : ⊦ ¬ j < i → max(j, i) = j])]]