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Proof step 20 from proof modify-sym (previous step)

r0 ∈ H0 ⊦ r0 ∈ rs, modify(rs)(H0[r0, o], H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ modify(rs)(H0, H1) ↔ (∃ r. ¬ r ∈ rs ∧ r ≠ null ∧ ¬ r ∈ H0 ∧ H1 = H0 ++ r) ∨ (∃ r, o. ¬ r ∈ rs ∧ r ∈ H0 ∧ H1 = H0[r, o]) ∨ (∃ r. ¬ r ∈ rs ∧ r ∈ H0 ∧ H1 = H0 -- r)
Proof step 22:
r0 ∈ H0 ⊦ r0 ∈ rs, (∃ r. ¬ r ∈ rs ∧ r ≠ null ∧ ¬ r ∈ H0[r0, o] ∧ H0 = H0[r0, o] ++ r) ∨ (∃ r, o0. ¬ r ∈ rs ∧ r ∈ H0[r0, o] ∧ H0 = H0[r0, o][r, o0]) ∨ (∃ r. ¬ r ∈ rs ∧ r ∈ H0[r0, o] ∧ H0 = H0[r0, o] -- r)

Rule argument

spec: <toplevel> name: modify seq: ⊦ modify(rs)(H0, H1) ↔ (∃ r. ¬ r ∈ rs ∧ r ≠ null ∧ ¬ r ∈ H0 ∧ H1 = H0 ++ r) ∨ (∃ r, o. ¬ r ∈ rs ∧ r ∈ H0 ∧ H1 = H0[r, o]) ∨ (∃ r. ¬ r ∈ rs ∧ r ∈ H0 ∧ H1 = H0 -- r) subst: [H1, H0, rs] → [H0, H0[r0, o], rs] flags: <all paths>

Additional information

Used terms: H0, H0[r0, o], rs