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Proof step 100 from proof reachable-addnew-rev (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 101:
⊦ reachable(r, r1, H) → (¬ reachable(r, H[r1].nxt, H) ↔ H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H)

Rule argument

spec: inst: 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[H[r0].nxt, ce]] flags: current, []

Additional information

Used simplifier rules: reachable-addnew: ⊦ reachable(r, r1, H) ∧ ¬ r2 ∈ H → (¬ reachable(r, r1, H[r2, ce]) ↔ false);%At-in-out: ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap] Used terms: r, r0, H[H[r0].nxt, ce]