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Proof step 191 from proof inv-gc (previous step)

gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2[nx.last]), inv(gstore2 \ jro0), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), valid-journal-head(nx, gstore2, jro0), nx.last ∈ gstore2, n1 ∈ gstore2, n1 ∈ gstore1, n1 ∈ dom gstore2 ∪ jro0, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1 ⊦ #(dom gstore2 ∪ jro0) = 0, jmaxino = 0, nx = [], pmaxino = 0, dom gstore2 ∪ jro0 = ∅, dups(nx), valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1), n1 ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 192:
⊦ 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 193:
gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(gstore2 \ jro0), inv(gstore2[nx.last]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(fi2), valid-journal-head(nx, gstore2, jro0), n1 ∈ dom gstore2 ∪ jro0, n1 ∈ gstore1, n1 ∈ gstore2, nx.last ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2 ⊦ #(dom gstore2 ∪ jro0) = 0, jmaxino = 0, nx = [], pmaxino = 0, dom gstore2 ∪ jro0 = ∅, dups(nx), n1 ∈ nx, nx ≠ [] ∧ nx.last ∈ gstore2 -- n1 ∧ ¬ nx.last ∈ jro0 ++ n1 ∧ ((gstore2 -- n1)[nx.last].gndlist = [] ∨ (gstore2 -- n1)[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] → [jro0 ++ n1, gstore2 -- n1, nx] flags: <all paths>

Additional information

Used terms: jro0 ++ n1, gstore2 -- n1, nx