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Proof step 6 from proof write-left (previous step)

r ∈ H0, H0 ⊥ H1 ⊦ (H0 ∪ H1)[r, o] = H0[r, o] ∪ H1, H1 ⊥ H0[r, o]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ H0 ⊥ H1 ↔ (∀ r. ¬ r ∈ H0 ∨ ¬ r ∈ H1)

Rule argument

spec: <toplevel> name: disj seq: ⊦ H0 ⊥ H1 ↔ (∀ r. ¬ r ∈ H0 ∨ ¬ r ∈ H1) subst: [H1, H0] → [H0[r, o], H1] flags: <all paths>

Additional information

Used simplifier rules: in-write: ⊦ r ∈ H[r0, o] ↔ r ∈ H;%disj-r: ⊦ r ∈ H1 ∧ H0 ⊥ H1 → (r ∈ H0 ↔ false); Used terms: H0[r, o], H1