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

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

Rule argument

[emptyarg]

Additional information

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