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Proof step 23 from proof add-preserves-reachable (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 24:
(H[r1].nxt ' + x).last = (H[r1].nxt ' + x0).last, H[r1].nxt = H[ce.nxt].nxt, path(H[r1].nxt ' + x, H[r1, ce]), reachable(H[r1].nxt, r1, H), (H[r1].nxt ' + x0).last ∈ H, ce.nxt ∈ H, path(H[r1].nxt ' + x0, H), r1 ∈ H ⊦ r1 = null, ce.nxt = null, reachable(r1, ce.nxt, H), path(r1 ' + ce.nxt ' + H[r1].nxt ' + x, H[r1, ce]) ∧ (r1 ' + ce.nxt ' + H[r1].nxt ' + x).last = (H[r1].nxt ' + x0).last

Rule argument

pos: right 4 terms: ce.nxt ' + H[r1].nxt ' + x abort: F discard: T computed: F

Additional information

Used terms: ce.nxt ' + H[r1].nxt ' + x