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Proof step 28 from proof add-preserves-reachable-rev (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 30:
¬ H[r].nxt ≠ r1, H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][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[r1, ce][H[r].nxt].nxt ' + x0).last = ce.nxt, r = null, H[r1, ce][H[r].nxt].nxt ' + x0 = [], r = r1, ce.nxt = null, r1 = null, reachable(r1, (H[r1, ce][H[r].nxt].nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H
Proof step 40:
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

Rule argument

spec: store inst: linheap name: At-other seq: ⊦ r ≠ r0 → H[r0, ce][r] = H[r] subst: [r, ce, r0, H] → [H[r].nxt, ce, r1, H] flags: rewrite

Additional information

Used terms: H[r].nxt, ce, r1, H