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Proof step 139 from proof inv-store (previous step)

gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), gstore3[m0] = groupblock(gndx, lax, m3), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore3[m0, groupblock(gndx, lax, m3 + m2)] \ jro0), inv(gstore3 \ jro0), inv(gstore2), inv(gstore3[nx.last]), key-cons(key, nd), refsize-cons(gstore3, range fi2), refsize-cons(gstore2, range fi1), ri-inj(fi2), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi1), valid-journal-head(nx, gstore3, jro0), m0 ∈ gstore3, @(m0, m1, m2) ∈ gstore3, nx.last ∈ gstore3, pmaxino ≤ max(key.ino + 1, jmaxino), pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2 ⊦ jmaxino = 0, max(key.ino + 1, jmaxino) = 0, nx = [], pmaxino = 0, dups(nx), valid-journal-head(nx, gstore3[m0, groupblock(gndx, lax, m3 + m2)], jro0), @(m0, m1, m2) ∈ fi2, key ∈ fi2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 140:
⊦ 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 141:
gstore3[m0] = groupblock(gndx, lax, m3), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore3[nx.last]), inv(gstore2), inv(gstore3 \ jro0), inv(gstore3[m0, groupblock(gndx, lax, m3 + m2)] \ jro0), key-cons(key, nd), refsize-cons(gstore2, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi1), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi2), valid-journal-head(nx, gstore3, jro0), nx.last ∈ gstore3, @(m0, m1, m2) ∈ gstore3, m0 ∈ gstore3, pmaxino ≤ jmaxino, pmaxino ≤ max(key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3 ⊦ jmaxino = 0, max(key.ino + 1, jmaxino) = 0, nx = [], pmaxino = 0, dups(nx), key ∈ fi2, @(m0, m1, m2) ∈ fi2, nx ≠ [] ∧ nx.last ∈ gstore3[m0, groupblock(gndx, lax, m3 + m2)] ∧ ¬ nx.last ∈ jro0 ∧ (gstore3[m0, groupblock(gndx, lax, m3 + m2)][nx.last].gndlist = [] ∨ gstore3[m0, groupblock(gndx, lax, m3 + m2)][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, gstore3[m0, groupblock(gndx, lax, m3 + m2)], nx] flags: <all paths>

Additional information

Used terms: jro0, gstore3[m0, groupblock(gndx, lax, m3 + m2)], nx