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Proof step 2 from proof write-unknown (conclusion)

⊦ rely(me, O1, H1[r, o1], O2, H2) → ((!(me, O2, r =>_) * P0)(H1) ↔ (!(me, O2, r => o1) * P0)(H1[r, o1]) ∧ r ∈ H1)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ rely(me, O1, H1[r, o1], O2, H2) → ((!(me, O2, r =>_ * P) * P0)(H1) ↔ (!(me, O2, r => o1 * P) * P0)(H1[r, o1]) ∧ r ∈ H1)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: write-unknown-p antecedent: succedent: rely(me, O1, H1[r, o1], O2, H2) → ( (!(me, O2, r =>_ * P) * P0)(H1) ↔ (!(me, O2, r => o1 * P) * P0)(H1[r, o1]) ∧ r ∈ H1) substlist: [me, O1, H1, r, o1, O2, H2, P, P0] → [me, O1, H1, r, o1, O2, H2, emp, P0] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ emp * P = P], [CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPSEQ : ⊦ P0 * P1 = P1 * P0])], [EXTRATERMS : (me, O1, H1, r, o1, O2, H2, emp, P0)]]