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Proof step 8 from proof reachable-addnew-rev (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0 ∧ ¬ dups(r ' + x))
Proof step 10:
r ∈ H, ∃ x. path(r ' + x, H[r2, ce]) ∧ (r ' + x).last = r2 ∧ ¬ dups(r ' + x) ⊦ r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null

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], r2, r] flags: rewrite, current

Additional information

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