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Proof step 49 from proof reachable-addnew-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
path(H[r].nxt ' + x0, H[H[r].nxt, ce]), r ∈ H, (H[r].nxt ' + x0).last ∈ H ⊦ H[r].nxt = null, r = H[r].nxt, r = null, reachable(ce.nxt, (H[r].nxt ' + x0).last, H), H[r].nxt ∈ H, r ∈ x0, H[r].nxt ∈ x0, dups(x0), reachable(r, (H[r].nxt ' + x0).last, H)

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%At-other: ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; from specification store[linheap]%in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]