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Proof step 12 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, dups(x1), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule exists right

And obtained the following new goals

Proof step 13:
path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, dups(x1), path(H[r0].nxt ' + (H[H[r0].nxt].nxt ' + x1) + H[r0].nxt ', H) ∧ ¬ r0 ∈ H[H[r0].nxt].nxt ' + x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

pos: right 7 terms: H[H[r0].nxt].nxt ' + x1 abort: F discard: F computed: F

Additional information

Used terms: H[H[r0].nxt].nxt ' + x1