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Proof step 56 from proof add-preserves-reachable-rev (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 57:
H[r1].nxt = H[ce.nxt].nxt, path(H[r1].nxt ' + x, H[r1, ce]), r1 ∈ H, (H[r1].nxt ' + x).last ∈ H[r1, ce], ce.nxt ∈ H ⊦ (H[r1].nxt ' + x).last = ce.nxt, ce.nxt = r1, ce.nxt = null, r1 = null, reachable(r1, ce.nxt, H), H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null, path(r1 ' + H[r1].nxt ', H) ∧ (r1 ' + H[r1].nxt ').last = (H[r1].nxt ' + x).last

Rule argument

pos: right 6 terms: H[r1].nxt ' abort: F discard: T computed: F

Additional information

Used terms: H[r1].nxt '