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Proof step 51 from proof rem-stays-reachable-aux1 (previous step)

¬ x ≠ [], path(H[H[(r1 ' + x).last].nxt].nxt ' + x0 + H[(r1 ' + x).last].nxt ', H), H[(r1 ' + x).last].nxt ∈ H, (r1 ' + x).last ∈ H, path(H[H[(r1 ' + x).last].nxt].nxt ' + x0 + H[(r1 ' + x).last].nxt ' + r1 ' + x, H), (r1 ' + x).last = r1 ∨ (r1 ' + x).last ∈ x ⊦ (r1 ' + x).last = H[(r1 ' + x).last].nxt, (r1 ' + x).last = H[H[(r1 ' + x).last].nxt].nxt, H[(r1 ' + x).last].nxt = null, H[(r1 ' + x).last].nxt = H[H[(r1 ' + x).last].nxt].nxt, dups((r1 ' + x).butlast), dups(x0), H[H[(r1 ' + x).last].nxt].nxt ∈ (r1 ' + x).butlast, H[H[(r1 ' + x).last].nxt].nxt ∈ x0, (r1 ' + x).last ∈ (r1 ' + x).butlast, dups(x0 + (r1 ' + x).butlast), H[(r1 ' + x).last].nxt ∈ (r1 ' + x).butlast, H[(r1 ' + x).last].nxt ∈ x0, (r1 ' + x).last ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
path(H[H[r1].nxt].nxt ' + x0 + H[r1].nxt ', H), H[r1].nxt ∈ H, r1 ∈ H, path(H[H[r1].nxt].nxt ' + x0 + H[r1].nxt ' + r1 ', H) ⊦ r1 = H[r1].nxt, r1 = H[H[r1].nxt].nxt, H[r1].nxt = null, H[r1].nxt = H[H[r1].nxt].nxt, H[H[r1].nxt].nxt ∈ x0, dups(x0), H[r1].nxt ∈ x0, r1 ∈ x0

Rule argument

Additional information

Used simplifier rules: in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]%b: ⊦ r '.butlast = []; from specification list-last[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]