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Proof step 12 from proof modified-stays-reachable (previous step)

(H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, ∀ r1, H0, ce0. path(r1 ' + x0, H0) → (∃ x1. path(r1 ' + x1, H0[(r1 ' + x1).last, ce0]) ∧ (r1 ' + x1).last = (r1 ' + x0).last) ⊦ r = null, ∃ x. path(r ' + x, H[(r ' + x).last, ce]) ∧ (r ' + x).last = (H[r].nxt ' + x0).last

User applied rule all left

And obtained the following new goals

Proof step 13:
(H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x0, H) → (∃ x1. path(H[r].nxt ' + x1, H[(H[r].nxt ' + x1).last, ce]) ∧ (H[r].nxt ' + x1).last = (H[r].nxt ' + x0).last) ⊦ r = null, ∃ x. path(r ' + x, H[(r ' + x).last, ce]) ∧ (r ' + x).last = (H[r].nxt ' + x0).last

Rule argument

pos: left 4 terms: H[r].nxt, H, ce abort: F discard: T computed: F

Additional information

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