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Proof step 40 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r0 ' + x + H[r0].nxt ', H[r0, ce]), path(r ' + x0 + r0 ', 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, H[r0].nxt = r0, r = H[r0].nxt, r = r0, dups(x1), dups(x0 + x), dups(x0), dups(x), r0 ∈ x0, r ∈ x1, r ∈ x0, r ∈ x, r0 ∈ x1, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ 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 41:
ce.nxt = H[H[r0].nxt].nxt, x = r1 + x2, path(r ' + x1 + r0 ', H), path(r ' + (x0 + r0 ' + x) + H[r0].nxt ', H[r0, ce]), path(r ' + x0 + r0 ', H[r0, ce]), path(r0 ' + x + H[r0].nxt ', H[r0, ce]), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = r0, H[r0].nxt = null, H[r0].nxt = ce.nxt, r = r0, r = H[r0].nxt, dups(x), dups(x0), dups(x0 + x), dups(x1), r0 ∈ x, H[r0].nxt ∈ x, H[r0].nxt ∈ x0, r0 ∈ x1, r ∈ x, r ∈ x0, r ∈ x1, r0 ∈ x0, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

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 [], +;;% ⊦ [] + x0 = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ∈ H[r, ce]; (s)% ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)% ⊦ H[r, ce][r] = ce; (s)