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Proof step 1 from proof aa (conclusion)

⊦ disj(x + y, x0 + y0) ↔ disj(x, x0) ∧ disj(x, y0) ∧ disj(y, x0) ∧ disj(y, y0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ disj(x, y + z) ↔ disj(x, y) ∧ disj(x, z)
Proof step 3:
⊦ disj(x + y, x0) ∧ disj(x + y, y0) ↔ disj(x, x0) ∧ disj(x, y0) ∧ disj(y, x0) ∧ disj(y, y0)

Rule argument

spec: inst: name: app-02 seq: ⊦ disj(x, y + z) ↔ disj(x, y) ∧ disj(x, z) subst: [z, y, x] → [y0, x0, x + y] flags: rewrite, current

Additional information

Used terms: y0, x0, x + y