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Proof step 24 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H, ∀ H0, r0, ce0, r2. H0[r0].nxt = H0[ce0.nxt].nxt ∧ reachable(r0, H0[r2].nxt, H0) ∧ path(r2 ' + x, H0[r0, ce0]) ∧ ce0.nxt ∈ H0 ∧ r0 ∈ H0 → ce0.nxt = null ∨ r0 = null ∨ x.last = ce0.nxt ∨ reachable(r0, ce0.nxt, H0) ∨ reachable(r0, x.last, H0) ⊦ r1 = null, ce.nxt = null, r = r1, x = [], r = null, x.last = ce.nxt, reachable(r1, ce.nxt, H), reachable(r1, x.last, H)

User applied rule all left

And obtained the following new goals

Proof step 25:
H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H, H[r1].nxt = H[ce.nxt].nxt ∧ reachable(r1, H[H[r].nxt].nxt, H) ∧ path(H[r].nxt ' + x, H[r1, ce]) ∧ ce.nxt ∈ H ∧ r1 ∈ H → ce.nxt = null ∨ r1 = null ∨ x.last = ce.nxt ∨ reachable(r1, ce.nxt, H) ∨ reachable(r1, x.last, H) ⊦ r1 = null, ce.nxt = null, r = r1, x = [], r = null, x.last = ce.nxt, reachable(r1, ce.nxt, H), reachable(r1, x.last, H)

Rule argument

pos: left 7 terms: H, r1, ce, H[r].nxt abort: F discard: T computed: T

Additional information

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