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Proof step 13 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r].nxt].nxt, (r ' + x0).last = H[r].nxt, path(r ' + x0, H[r, ce]), H[r].nxt ∈ H, r ∈ H, H[r].nxt ∈ H[r, ce] ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = null, r ∈ x0, dups(x0), ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

User applied rule constructor cut

And obtained the following new goals

Proof step 14:
x0 = r0 + x1, ce.nxt = H[H[r].nxt].nxt, (r ' + x0).last = H[r].nxt, path(r ' + x0, H[r, ce]), H[r].nxt ∈ H, r ∈ H, H[r].nxt ∈ H[r, ce] ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = null, r ∈ x0, dups(x0), ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%reflist freely generated by [], +;;%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]