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Proof step 26 from proof reachable-addnew-rev (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0 ∧ ¬ dups(r ' + x))
Proof step 28:
∃ x. path(r ' + x, H[r2, ce]) ∧ (r ' + x).last = r1 ∧ ¬ dups(r ' + x), r ∈ H, r1 ∈ H ⊦ reachable(r, r1, H), r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, r1, H)

Rule argument

spec: inst: name: reachable-nodups-def seq: ⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0 ∧ ¬ dups(r ' + x)) subst: [H, r0, r] → [H[r2, ce], r1, r] flags: rewrite, current

Additional information

Used terms: H[r2, ce], r1, r