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Proof step 212 from proof rem-stays-reachable-aux2 (previous step)

path(r ' + x + H[r0].nxt ', H), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, r0 = r, reachable(r, (r ' + x).last, H), r0 ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 213:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 214:
path(r ' + x + H[r0].nxt ', H), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, r0 = r, ∃ x0. path(r ' + x0, H) ∧ (r ' + x0).last = (r ' + x).last, r0 ∈ x

Rule argument

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

Additional information

Used terms: H, (r ' + x).last, r