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Proof step 11 from proof changenonnxt-reachable (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 13:
¬ r ≠ r1, ce.nxt = H[r1].nxt, (H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r1, ce], ∀ ce0, H0, r2, r3. ce0.nxt = H0[r2].nxt ∧ path(r3 ' + x0, H0) → path(r3 ' + x0, H0[r2, ce0]) ⊦ r = null, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]) ∧ H[r1, ce][r].nxt = H[r].nxt
Proof step 15:
r ≠ r1, ce.nxt = H[r1].nxt, (H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r1, ce], ∀ ce0, H0, r2, r3. ce0.nxt = H0[r2].nxt ∧ path(r3 ' + x0, H0) → path(r3 ' + x0, H0[r2, ce0]) ⊦ r = null, path(H[r].nxt ' + x0, H[r1, ce]) ∧ H[r].nxt = H[r].nxt

Rule argument

spec: store inst: linheap name: At-other seq: ⊦ r ≠ r0 → H[r0, ce][r] = H[r] subst: [r, ce, r0, H] → [r, ce, r1, H] flags: rewrite

Additional information

Used terms: r, ce, r1, H