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Proof step 8 from proof modnotreachable-reachable-rev (previous step)

path(H[r0, ce][r].nxt ' + x0, H[r0, ce]), r ∈ H[r0, ce], (H[r0, ce][r].nxt ' + x0).last ∈ H[r0, ce], r0 ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0[r3, ce0]) ∧ r3 ∈ H0 → reachable(r2, r3, H0) ∨ reachable(r2, (r2 ' + x0).last, H0) ⊦ r = null, reachable(r, (H[r0, ce][r].nxt ' + x0).last, H), reachable(r, r0, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 10:
path(H[r].nxt ' + x0, H[r0, ce]), r0 ∈ H, (H[r].nxt ' + x0).last ∈ H[r0, ce], r ∈ H[r0, ce], ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0[r3, ce0]) ∧ r3 ∈ H0 → reachable(r2, r3, H0) ∨ reachable(r2, (r2 ' + x0).last, H0) ⊦ r = null, r = r0, reachable(r, r0, H), reachable(r, (H[r].nxt ' + x0).last, 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, r0, H] flags: <all paths>

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ r ≠ null ∧ r ∈ H;% ⊦ r ∈ H[r, ce]; (s)% ⊦ H[r, ce][r] = ce; (s) Used terms: r, ce, r0, H