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Proof step 40 from proof add-preserves-reachable-rev (previous step)

H[r].nxt ≠ r1, H[r1].nxt = H[ce.nxt].nxt, path(H[H[r].nxt].nxt ' + x0, H[r1, ce]), H[r].nxt ∈ H[r1, ce], ce.nxt ∈ H, r1 ∈ H, reachable(r1, H[r].nxt, H), r ∈ H ⊦ H[r].nxt = null, (H[H[r].nxt].nxt ' + x0).last = ce.nxt, r = null, H[H[r].nxt].nxt ' + x0 = [], r = r1, ce.nxt = null, r1 = null, reachable(r1, (H[H[r].nxt].nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
H[r1].nxt = H[ce.nxt].nxt, ce.nxt ∈ H, r1 ∈ H, reachable(r1, H[r].nxt, H), r ∈ H, path(H[H[r].nxt].nxt ' + x0, H[r1, ce]), H[r].nxt ∈ H ⊦ H[r].nxt = null, (H[H[r].nxt].nxt ' + x0).last = ce.nxt, r = null, H[H[r].nxt].nxt ' + x0 = [], r = r1, ce.nxt = null, r1 = null, H[r].nxt = r1, reachable(r1, (H[H[r].nxt].nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

Rule argument

Additional information

Used simplifier rules: In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]