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Proof step 4 from proof reachable-addnew-rev (previous step)

reachable(r, r1, H[r2, ce]), r ∈ H, r1 ∈ H[r2, ce] ⊦ reachable(r, r1, H), r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ (r1 = H[r0].nxt ∨ reachable(ce.nxt, r1, H))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H
Proof step 6:
reachable(r, r1, H[r2, ce]), r ∈ H, r1 = r2 ∨ r1 ∈ H ⊦ reachable(r, r1, H), r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ (r1 = H[r0].nxt ∨ reachable(ce.nxt, r1, H))

Rule argument

spec: store inst: linheap name: In-insert seq: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H subst: [ce, r0, H, r] → [ce, r2, H, r1] flags: rewrite

Additional information

Used terms: ce, r2, H, r1