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Proof step 17 from proof k-reachable-def (previous step)

path(H[r].nxt ' + x0, H), r ∈ H, ∀ r0, H0. path(r0 ' + x0, H0) → r0 = null ∨ (∃ n. reachable-n(H0, n, r0, x0.last)) ⊦ x0 = [], r = null, ∃ n. reachable-n(H, n, r, x0.last)

User applied rule all left

And obtained the following new goals

Proof step 18:
path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x0, H) → H[r].nxt = null ∨ (∃ n. reachable-n(H, n, H[r].nxt, x0.last)) ⊦ x0 = [], r = null, ∃ n. reachable-n(H, n, r, x0.last)

Rule argument

pos: left 3 terms: H[r].nxt, H abort: F discard: T computed: T

Additional information

Used terms: H[r].nxt, H