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Proof step 7 from proof modnotreachable-reachable-rev (previous step)

(H[r0, ce][r].nxt ' + x0).last ∈ H[r0, ce], path(H[r0, ce][r].nxt ' + x0, H[r0, ce]), r ∈ H[r0, ce], r0 ∈ H, ∀ r2, H0, r3, ce0. r2 ∈ H0 ∧ path(r3 ' + x0, H0[r2, ce0]) → reachable(r3, (r3 ' + x0).last, H0) ∨ reachable(r3, r2, 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 8:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 9:
r ≠ r0, (H[r].nxt ' + x0).last ∈ H[r0, ce], path(H[r].nxt ' + x0, H[r0, ce]), r ∈ H[r0, ce], r0 ∈ H, ∀ r2, H0, r3, ce0. r2 ∈ H0 ∧ path(r3 ' + x0, H0[r2, ce0]) → reachable(r3, (r3 ' + x0).last, H0) ∨ reachable(r3, r2, H0) ⊦ r = null, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, r0, 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: rewrite

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap] Used terms: r, ce, r0, H