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Proof step 4 from proof free-unknown (previous step)

((r =>_ * P))(H) ⊦ P(H -- r)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ H1 ≡ H0 -- r → (((r =>_ * P))(H0) ↔ P(H1) ∧ r ∈ H0)

Rule argument

spec: separation name: free-unknown seq: ⊦ H1 ≡ H0 -- r → (((r =>_ * P))(H0) ↔ P(H1) ∧ r ∈ H0) subst: [H1, H0, P, r] → [H -- r, H, P, r] flags: <all paths>

Additional information

Used simplifier rules: ⊦ H ≡ H; (s) Used terms: H -- r, H, P, r