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Proof step 11 from proof reachable-addnewtonull-rev (previous step)

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

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

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, r2, H] flags: rewrite

Additional information

Used simplifier rules: null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: r, ce, r2, H