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Proof step 9 from proof min-del-nlz-01 (previous step)

min((i ' + ints0) -l i0) < 0, min((i ' + ints0) -l i0) < min(i, min(ints0)), min((i ' + ints0) -l i0) < min(ints0), 0 < min(i, min(ints0)), 0 < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i ≠ i0 → (i0 ' + ints) -l i = i0 ' + (ints -l i)
Proof step 11:
¬ i0 ≠ i, min((i ' + ints0) -l i0) < 0, min((i ' + ints0) -l i0) < min(i, min(ints0)), min((i ' + ints0) -l i0) < min(ints0), 0 < min(i, min(ints0)), 0 < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = []
Proof step 13:
i0 ≠ i, min(i ' + (ints0 -l i0)) < 0, min(i ' + (ints0 -l i0)) < min(i, min(ints0)), min(i ' + (ints0 -l i0)) < min(ints0), 0 < min(i, min(ints0)), 0 < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = []

Rule argument

spec: list-del inst: intlista name: del-n seq: ⊦ i ≠ i0 → (i0 ' + ints) -l i = i0 ' + (ints -l i) subst: [i, ints, i0] → [i0, ints0, i] flags: rewrite

Additional information

Used terms: i0, ints0, i