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Proof step 12 from proof sum-in-not-ls (previous step)

Σ ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0, ∀ j0. ¬ j0 ∈ ints0 ∨ ¬ Σ ints0 < j0 ∨ (∃ i. ¬(i ∈ ints0 → 0 ≤ i)) ⊦ i ∈ ints0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
∀ i. i ∈ ints → 0 ≤ i ⊦ ¬ Σ ints < 0
Proof step 14:
¬(∀ i. i ∈ ints0 → 0 ≤ i), Σ ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0, ∀ j0. ¬ j0 ∈ ints0 ∨ ¬ Σ ints0 < j0 ∨ (∃ i. ¬(i ∈ ints0 → 0 ≤ i)) ⊦ i ∈ ints0

Rule argument

spec: inst: name: sum-not-ls-zero seq: ∀ i. i ∈ ints → 0 ≤ i ⊦ ¬ Σ ints < 0 subst: [ints] → [ints0] flags: rewrite, current

Additional information

Used terms: ints0