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Proof step 16 from proof linearity (previous step)

r1 ∈ H, path(r ' + x1 + H[(r ' + x1).last].nxt ', H), reachable(r, r1, H), H[(r ' + x1).last].nxt ∈ H, path(r ' + x1, H), reachable((r ' + x1).last, r1, H), ∀ x0, r2, H0, r1. # x0 < #(x1 + H[(r ' + x1).last].nxt ') → path(r2 ' + x0, H0) ∧ reachable(r2, r1, H0) ∧ (r2 ' + x0).last ∈ H0 ∧ r1 ∈ H0 → reachable((r2 ' + x0).last, r1, H0) ∨ reachable(r1, (r2 ' + x0).last, H0) ⊦ H[(r ' + x1).last].nxt = null, reachable(H[(r ' + x1).last].nxt, r1, H), reachable(r1, H[(r ' + x1).last].nxt, H), reachable(r1, (r ' + x1).last, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: fromnext-reachable seq: ⊦ reachable(r, r0, H) ∧ r ≠ r0 → (¬ reachable(H[r].nxt, r0, H) ↔ false) subst: [r0, r, H] → [r1, (r ' + x1).last, H] flags: rewrite, current

Additional information

Used terms: r1, (r ' + x1).last, H