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Proof step 11 from proof reach-n-path-n (previous step)

H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = null, r = null, ∃ x. path(x, H) ∧ hd x = r ∧ x.last = H[hd x].nxt ∧ # x = 2

User applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: r ' + H[r].nxt ' abort: F discard: T computed: F

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0;%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ hd(r ' + x0) = r; (s)% ⊦ (x0 + r ').last = r; (s)% ⊦ #(x0 + x1) = # x0 + # x1; (s)% ⊦ # r ' = 0 +1; (s) Used terms: r ' + H[r].nxt '