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Proof step 5 from proof max-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i < max(i0 ' + x), i0 ≤ i, i0 < max(i0 ' + x), ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ max(x0) ∈ x0) ⊦ max(i0 ' + x) ∈ x

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [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])]]