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Proof step 2 from proof product-equal-01 (previous step)

∀ i. i ∈ ints ↔ i ∈ ints0 ⊦ Π ints = Π ints0, dups(ints), dups(ints0)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ perm(ints, ints0) → Π ints = Π ints0
Proof step 4:
perm(ints, ints0) → Π ints = Π ints0, ∀ i. i ∈ ints ↔ i ∈ ints0 ⊦ Π ints = Π ints0, dups(ints), dups(ints0)

Rule argument

spec: inst: name: product-perm-equal seq: ⊦ perm(ints, ints0) → Π ints = Π ints0 subst: [ints, ints0] → [ints, ints0] flags: current, []

Additional information

Used terms: ints, ints0