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Proof step 23 from proof min-rec (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 24:
min(i ' + ints) ∈ i ' + ints, min(i ' + ints) ≤ i, min(ints) ≤ i, min(i ' + ints) < min(ints), min(i ' + ints) < i, ∀ i. i ∈ ints → min(ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0 ⊦ ints = [], min(i ' + ints) = min(ints), min(i ' + ints) ∈ ints

Rule argument

fma: min(i ' + ints) ∈ i ' + ints

Additional information

Used simplifier rules: min-in: ⊦ min(ints) ∈ ints ↔ ints ≠ [];%e-01: ⊦ i ' + ints ≠ []; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista] Used formulas: min(i ' + ints) ∈ i ' + ints