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Proof step 13 from proof min-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i < i0, ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(min(i0 ' + x), i) = i, min(min(i0 ' + x), i) = i0, min(min(i0 ' + x), i) ∈ x

Rule argument

[emptyarg]

Additional information

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