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Proof step 39 from proof acyclic-rem-not-reachable (previous step)

x1 = r0 + x, ce.nxt = H[H[r].nxt].nxt, r ∈ H, path(r ' + x1 + H[r].nxt ', H[r, ce]), H[r].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = null, r = H[r].nxt, r = null, r ∈ x1, H[r].nxt ∈ x1, dups(x1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
ce.nxt = H[H[r].nxt].nxt, path(ce.nxt ' + x + H[r].nxt ', H[r, ce]), r ∈ H, H[r].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = ce.nxt, r = ce.nxt, r = null, r = H[r].nxt, H[r].nxt = null, dups(x), ce.nxt ∈ x, H[r].nxt ∈ x, r ∈ x

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%rec: ⊦ dups(r ' + x0) ↔ ¬ ¬(r ∈ x0 ∨ dups(x0)); from specification list-dup[reflist]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]