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Proof step 26 from proof rem-stays-reachable-aux1 (previous step)

path(H[r0].nxt ' + x + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, r0 ∈ x, reachable(H[H[r0].nxt].nxt, H[r0].nxt, H) ∧ ¬ reachable(H[H[r0].nxt].nxt, r0, H)

User applied rule constructor cut

And obtained the following new goals

Proof step 27:
x = r + x0, path(H[r0].nxt ' + x + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, r0 ∈ x, reachable(H[H[r0].nxt].nxt, H[r0].nxt, H) ∧ ¬ reachable(H[H[r0].nxt].nxt, r0, H)

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]