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Proof step 12 from proof modnotreachable-reachable (previous step)

path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r1, ce], ∀ r, H, r1, ce. path(r ' + x0, H) → path(r ' + x0, H[r1, ce]) ∨ reachable(r, r1, H) ⊦ r = null, reachable(r, r1, H), 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 13:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 14:
path(H[r].nxt ' + x0, H), r ∈ H[r1, ce], r ∈ H, ∀ r, H, r1, ce. path(r ' + x0, H) → path(r ' + x0, H[r1, ce]) ∨ reachable(r, r1, H) ⊦ r = null, r = r1, reachable(r, r1, H), 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: <all paths>

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ r ≠ null ∧ r ∈ H; Used terms: r, ce, r1, H