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Proof step 5 from proof cons-03 (previous step)

disj(x, y), disj(x + a ', y), a ∈ y ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ disj(x, y) ↔ (∀ a. ¬(a ∈ x ∧ a ∈ y))
Proof step 7:
disj(x, y), a ∈ y, ∀ a0. ¬(a0 ∈ x + a ' ∧ a0 ∈ y) ⊦

Rule argument

spec: <toplevel> name: disjoint seq: ⊦ disj(x, y) ↔ (∀ a. ¬(a ∈ x ∧ a ∈ y)) subst: [y, x] → [y, x + a '] flags: <all paths>

Additional information

Used terms: y, x + a '