[Imprint][Data Privacy Statement][E-Mail]

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Proof step 7 from proof product-divide (previous step)

perm(ints2, (ints0 + ints1) -1l i), ∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1 ⊦ i * Π ints2 = Π ints0 * Π ints1, ¬ i ∈ ints0 ∧ ¬ i ∈ ints1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ i ∈ ints → (ints + ints0) -1l i = ints + (ints0 -1l i)
Proof step 9:
¬ ¬ i ∈ ints0, perm(ints2, (ints0 + ints1) -1l i), ∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1 ⊦ i * Π ints2 = Π ints0 * Π ints1, ¬ i ∈ ints0 ∧ ¬ i ∈ ints1
Proof step 13:
¬ i ∈ ints0, perm(ints2, ints0 + (ints1 -1l i)), ∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1 ⊦ i * Π ints2 = Π ints0 * Π ints1, ¬ i ∈ ints0 ∧ ¬ i ∈ ints1

Rule argument

spec: list-del inst: intlista name: app-01 seq: ⊦ ¬ i ∈ ints → (ints + ints0) -1l i = ints + (ints0 -1l i) subst: [i, ints0, ints] → [i, ints1, ints0] flags: rewrite

Additional information

Used terms: i, ints1, ints0