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Proof step 3 from proof rem-stays-reachable-aux2 (previous step)

H[r0].nxt = H[r1].nxt, reachable(r, r1, H), reachable(r, r0, H), H[r1].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r1].nxt = null, reachable(r0, r1, H), ∃ x. path(r ' + x + H[r1].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 5:
H[r0].nxt = H[r1].nxt, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r1, reachable(r, r0, H), H[r1].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r1].nxt = null, reachable(r0, r1, H), ∃ x. path(r ' + x + H[r1].nxt ', H) ∧ ¬ 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, r1, r] flags: rewrite, current

Additional information

Used terms: H, r1, r