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Proof step 3 from proof ls-inv-reduce-jnlhead (previous step)

inv(gstore \ ns), valid-journal-head(nx, gstore, ns) ⊦ inv(gstore[nx.last, gblock] \ ns) ↔ inv(gblock), nx = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ (gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end)

Rule argument

spec: gjournal-base name: valid-journal-head seq: ⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ ( gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end) subst: [ginval, gstore, nx] → [ns, gstore, nx] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inv(gstore \ ns) → (inv(gstore[n, gblock] \ ns) ↔ n ∈ ns ∨ inv(gblock)); (ws) Used terms: ns, gstore, nx