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Proof step 84 from proof reachable-addnew-rev (previous step)

reachable(ce.nxt, r1, H[H[r0].nxt, ce]), reachable(r, r0, H[H[r0].nxt, ce]), reachable(r, r0, H), r ∈ H, r0 ∈ H, r0 ∈ H[H[r0].nxt, ce], r1 ∈ H[H[r0].nxt, ce], r1 = H[r0].nxt ∨ reachable(ce.nxt, r1, H) ⊦ H[r0].nxt = null, reachable(r, r1, H[H[r0].nxt, ce]), reachable(r, r1, H), H[r0].nxt ∈ H

User applied rule insert lemma

And obtained the following new goals

Proof step 85:
⊦ reachable(r, r0, H) ∧ reachable(r0, r1, H) → reachable(r, r1, H)
Proof step 86:
reachable(r, r0, H[H[r0].nxt, ce]) ∧ reachable(r0, r1, H[H[r0].nxt, ce]) → reachable(r, r1, H[H[r0].nxt, ce]), reachable(ce.nxt, r1, H[H[r0].nxt, ce]), reachable(r, r0, H[H[r0].nxt, ce]), reachable(r, r0, H), r ∈ H, r0 ∈ H, r0 ∈ H[H[r0].nxt, ce], r1 ∈ H[H[r0].nxt, ce], r1 = H[r0].nxt ∨ reachable(ce.nxt, r1, H) ⊦ H[r0].nxt = null, reachable(r, r1, H[H[r0].nxt, ce]), reachable(r, r1, H), H[r0].nxt ∈ H

Rule argument

spec: inst: name: reachable-trans seq: ⊦ reachable(r, r0, H) ∧ reachable(r0, r1, H) → reachable(r, r1, H) subst: [r, r0, H, r1] → [r, r0, H[H[r0].nxt, ce], r1] flags: current, []

Additional information

Used terms: r, r0, H[H[r0].nxt, ce], r1