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Proof step 77 from proof rem-stays-reachable-aux (previous step)

path(r ' + x2 + r0 ', H[r0, ce]), path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r0 ∈ x1, r ∈ x2, r0 ∈ x2, dups(x2), path(r ' + x2 + (r0 + (x1 + H[r0].nxt)), H[r0, ce]) ∧ (r ' + x2 + (r0 + (x1 + H[r0].nxt))).last = H[r0].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + r0 ', H[r0, ce]), path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r0 ∈ x1, r ∈ x2, r0 ∈ x2, dups(x2), path(r ' + x2 + r0 ' + x1 + H[r0].nxt ', H[r0, ce])

Rule argument

Additional information

Used simplifier rules: last-01: ⊦ (r ' + x0 + r0 ').last = r0; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%Last: ⊦ x0 + r = x0 + r '; from specification list[reflist]