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Proof step 5 from proof modify-sym (previous step)

¬ r ∈ rs ∧ r ≠ null ∧ ¬ r ∈ H0 ∧ H1 = H0 ++ r ∨ ¬ r0 ∈ rs ∧ r0 ∈ H0 ∧ H1 = H0[r0, o] ∨ ¬ r1 ∈ rs ∧ r1 ∈ H0 ∧ H1 = H0 -- r1 ⊦ modify*(rs)(H1, H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ modify*(rs)(H0, H1) ↔ modify(rs) ^*(H0, H1)
Proof step 7:
¬ r ∈ rs ∧ r ≠ null ∧ ¬ r ∈ H0 ∧ H1 = H0 ++ r ∨ ¬ r0 ∈ rs ∧ r0 ∈ H0 ∧ H1 = H0[r0, o] ∨ ¬ r1 ∈ rs ∧ r1 ∈ H0 ∧ H1 = H0 -- r1 ⊦ modify(rs) ^*(H1, H0)

Rule argument

spec: <toplevel> name: modify+ seq: ⊦ modify*(rs)(H0, H1) ↔ modify(rs) ^*(H0, H1) subst: [H1, H0, rs] → [H0, H1, rs] flags: <all paths>

Additional information

Used terms: H0, H1, rs