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Proof step 6 from proof min-in (previous step)

i ' + x = [] ∨ min(i ' + x) ∈ i ' + x, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
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, min(i ' + x) ≠ i ∧ ¬ min(i ' + x) ∈ x

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ d0 ' ↔ d = d0], [CSIMPSEQ : ⊦ d ∈ x + y ↔ ¬ ¬ (d ∈ x ∨ d ∈ y)], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d ' + x ≠ []])]]