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Proof step 39 from proof rem-stays-reachable-aux (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 40:
x = r1 + x2, ce.nxt = H[H[r0].nxt].nxt, path(r ' + x0 + r0 ', H[r0, ce]), path(r0 ' + x + H[r0].nxt ', H[r0, ce]), path(r ' + (x0 + r0 ' + x) + H[r0].nxt ', H[r0, ce]), path(r ' + x1 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = H[r0].nxt, r = r0, H[r0].nxt = r0, r0 ∈ x0, r ∈ x1, r0 ∈ x1, dups(x1), r ∈ x0, r ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x, dups(x0 + x), dups(x0), dups(x), ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

var: x

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ ¬ ¬(r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0);%reflist freely generated by [], +;;%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]