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Proof step 14 from proof modified-stays-reachable (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 15:
(H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, (H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x, H[(H[r].nxt ' + x0).last, ce]) ⊦ r = null, path(r ' + H[r].nxt ' + x, H[(r ' + H[r].nxt ' + x).last, ce]) ∧ (r ' + H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, ∃ x. path(r ' + x, H[(r ' + x).last, ce]) ∧ (r ' + x).last = (H[r].nxt ' + x0).last

Rule argument

pos: right 2 terms: H[r].nxt ' + x abort: F discard: F computed: F

Additional information

Used terms: H[r].nxt ' + x