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Proof step 9 from proof min-rec (previous step)

ints ≠ [] → min(ints) ∈ ints ∧ (∀ i. i ∈ ints → min(ints) ≤ i), min(i ' + ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0 ⊦ ints = [], min(i ' + ints) = min(i, min(ints))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
min(i ' + ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ i. i ∈ ints → min(ints) ≤ i ⊦ ints = [], min(i ' + ints) = min(i, min(ints))

Rule argument

Additional information

Used simplifier rules: min-in: ⊦ min(ints) ∈ ints ↔ ints ≠ [];