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Proof step 7 from proof add-preserves-reachable (previous step)

H[r1].nxt = H[ce.nxt].nxt, (H[r].nxt ' + x0).last ∈ H, reachable(r, r1, H), ce.nxt ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r1 ∈ H, ∀ H0, r2, ce0, r3. H0[r2].nxt = H0[ce0.nxt].nxt ∧ path(r3 ' + x0, H0) ∧ ce0.nxt ∈ H0 ∧ reachable(r3, r2, H0) → ce0.nxt = null ∨ reachable(r3, (r3 ' + x0).last, H0[r2, ce0]) ∨ reachable(r3, ce0.nxt, H0) ⊦ r = null, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce]), reachable(r, ce.nxt, H)

User applied rule all left

And obtained the following new goals

Proof step 8:
H[r1].nxt = H[ce.nxt].nxt, (H[r].nxt ' + x0).last ∈ H, reachable(r, r1, H), ce.nxt ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r1 ∈ H, H[r1].nxt = H[ce.nxt].nxt ∧ path(H[r].nxt ' + x0, H) ∧ ce.nxt ∈ H ∧ reachable(H[r].nxt, r1, H) → ce.nxt = null ∨ reachable(H[r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]) ∨ reachable(H[r].nxt, ce.nxt, H) ⊦ r = null, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce]), reachable(r, ce.nxt, H)

Rule argument

pos: left 8 terms: H, r1, ce, H[r].nxt abort: F discard: T computed: T

Additional information

Used terms: H, r1, ce, H[r].nxt