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Proof step 8 from proof max-ge (previous step)

x1 = i1 + x, max(i0 ' + x1) < i, ∀ x0, i. # x0 < # (i0 + x1) → (i ∈ x0 ∧ max(x0) < i → false) ⊦ i ≠ i0 ∧ ¬ i ∈ x1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ max(i ' + j ' + x) = max(max(i, j), max(min(i, j) ' + x))
Proof step 7:
i0 < i, i1 < i, max(min(i0, i1) ' + x) < i, i ∈ x, ∀ x0, i. # x0 < # (i0 + i1 + x) → (i ∈ x0 ∧ max(x0) < i → false) ⊦ i = i1, i = i0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < 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) = j], [CSIMPSEQ : ⊦ d ∈ d0 ' ↔ d = d0], [CSIMPSEQ : ⊦ d ∈ x + y ↔ ¬ ¬ (d ∈ x ∨ d ∈ y)], [CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ max(i, max(j, j0)) = max(max(i, j), j0)], [CSIMPSEQ : ⊦ max(i, j) < j0 ↔ i < j0 ∧ j < j0], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d + x = d ' + x])]]