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Proof step 19 from proof k-reachable-def (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 20:
path(H[r].nxt ' + x0, H), reachable-n(H, n, H[r].nxt, x0.last), r ∈ H ⊦ r = null, x0 = [], ∃ n. reachable-n(H, n, r, x0.last)

Rule argument

pos: left 3

Additional information

Used simplifier rules: null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]