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

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

Rule argument

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

Additional information

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