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Proof step 2 from proof valid-journal-head-valid-group-nodes (previous step)

gstore[nx.last] = groupblock(gndx, lax, lnum), valid-journal-head(nx, gstore, ginval) ⊦ nx = [], valid-group-nodes(gndx) = # gndx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ (gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end)
Proof step 4:
gstore[nx.last] = groupblock(gndx, lax, lnum), nx.last ∈ gstore, gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end ⊦ nx = [], valid-group-nodes(gndx) = # gndx, nx.last ∈ ginval

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] → [ginval, gstore, nx] flags: <all paths>

Additional information

Used terms: ginval, gstore, nx