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Proof step 12 from proof reachable-addnewtonull-rev (previous step)

ce.nxt = null, path(H[r2, ce][r].nxt ' + x0, H[r2, ce]), r ∈ H[r2, ce], (H[r2, ce][r].nxt ' + x0).last ∈ H, ∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H → path(r ' + x0, H) ∨ r2 ∈ H ⊦ 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 13:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 14:
ce.nxt = null, path(H[r].nxt ' + x0, H[r2, ce]), (H[r].nxt ' + x0).last ∈ H, r ∈ H[r2, ce], ∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H → path(r ' + x0, H) ∨ r2 ∈ H ⊦ r = null, r = r2, 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: <all paths>

Additional information

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