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

ce.nxt = null, reachable(r, r1, H[r2, ce]), r1 ∈ H, r1 ∈ H[r2, ce] ⊦ r2 ∈ H, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 6:
ce.nxt = null, ∃ x. path(r ' + x, H[r2, ce]) ∧ (r ' + x).last = r1, r1 ∈ H, r1 ∈ H[r2, ce] ⊦ r2 ∈ H, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r1

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[r2, ce], r1, r] flags: rewrite, current

Additional information

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