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Proof step 8 from proof removed-stays-reachable (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
⊦ reachable(r, r1, H) → (reachable(r, H[r1].nxt, H) ↔ ¬(H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H))

Rule argument

spec: <toplevel> name: reach-reachnext seq: ⊦ reachable(r, r1, H) → ( reachable(r, H[r1].nxt, H) ↔ ¬(H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H)) subst: [r, r1, H] → [r, r0, H[r0, ce]]

Additional information

Used simplifier rules: changenonnxt-reachable: ⊦ reachable(r, r0, H) ∧ ce.nxt = H[r1].nxt → (reachable(r, r0, H[r1, ce]) ↔ true);%endnotinH-notreachable: ⊦ ¬ r0 ∈ H → (reachable(r, r0, H) ↔ false);% ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws) Used terms: r, r0, H[r0, ce]