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Proof step 15 from proof rem-stays-reachable-aux2 (previous step)

H[r0].nxt = H[(r0 ' + x0).last].nxt, r0 ∈ H, path(r ' + x1 + r0 ' + x0, H), reachable(r, r0, H), H[r0].nxt ∈ H, (r0 ' + x0).last ∈ H ⊦ H[r0].nxt = null, reachable(r0, (r0 ' + x0).last, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 17:
H[r0].nxt = H[(r0 ' + x0).last].nxt, r0 ∈ H, path(r ' + x1 + r0 ' + x0, H), reachable(r, r0, H), H[r0].nxt ∈ H, (r0 ' + x0).last ∈ H ⊦ H[r0].nxt = null, ∃ x. path(r0 ' + x, H) ∧ (r0 ' + x).last = (r0 ' + x0).last

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, (r0 ' + x0).last, r0] flags: rewrite, current

Additional information

Used terms: H, (r0 ' + x0).last, r0