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Proof step 19 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, ∃ x, x2. x1 = x + (r0 + x2) ⊦ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
path(H[H[r0].nxt].nxt ' + x0 + (r0 ' + x) + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, H[H[r0].nxt].nxt = r0, H[r0].nxt = r0, dups(x0 + x), dups(x0), dups(x), reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x0, H[H[r0].nxt].nxt ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x0, r0 ∈ x, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]% ⊦ dups(x0 + r ' + x1) ↔ r ∈ x0 ∨ r ∈ x1 ∨ dups(x0 + x1); (ws)% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)