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Proof step 15 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, dups(x1), reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, r0 ≠ H[H[r0].nxt].nxt ∧ ¬ r0 ∈ x1

User applied rule case distinction

And obtained the following new goals

Proof step 16:
path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ x1, H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = H[H[r0].nxt].nxt, dups(x1), reachable(H[H[r0].nxt].nxt, r0, H), H[r0].nxt ∈ x1, H[H[r0].nxt].nxt ∈ x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

pos: right 8

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ r ≠ null ∧ r ∈ H;%path-first-in-H: ⊦ path(r ' + x, H) → (r ∈ H ↔ true);%null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]