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Proof step 66 from proof inv-gc-update-index (previous step)

# ax3 = # ndx2, # ax2 = # ndx1, gstore3[@(m, m0, m1)] = mkgnode(nd, m2, boolvar, boolvar0), fi2[ndx2.keys, ax3][nd.key] = @(m3, m4, m5), gstore3[m3] = groupblock(gndx, lax, n1 + m5), gstore3[m3, groupblock(gndx, lax, n1)][m] = groupblock(gndx0, lax0, m6), abs-log(nx, gstore3 ↓) = abs-log(nx, gstore2 ↓), dom gstore3 = dom gstore2, nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, range fi2 ∩ ax2.toSet = ∅, range fi2 ∩ ax3.toSet = ∅, dom gstore1 ∪ elems nx = (dom gstore2 ∪ jro0) ++ m, fi2[ndx2.keys, ax3].inos ∪ (nd.key.inode? ⊃ ∅ ++ nd.key.ino;∅) < max(nd.key.ino + 1, jmaxino), fi1.inos < pmaxino, fi2[ndx2.keys, ax3].inos < jmaxino, p_os < pmaxino, fi2.inos < jmaxino1, jro1 < jmaxino1, gstore3[m3, groupblock(gndx, lax, n1)][m, groupblock(gndx0, lax0, m6 + m1)] =○refsize gstore3, inv(gstore3[m3, groupblock(gndx, lax, n1)][m, groupblock(gndx0, lax0, m6 + m1)] \ jro0), inv(gstore3 \ jro0), inv(gstore1), inv(gstore2 \ jro0), key-cons(nd.key, nd), key-cons(ndx2), key-cons(ndx1), nodes-cons(ax3 + @(m, m0, m1) ' + ax2, ndx2 + nd ' + ndx1, gstore2, jro0), nodes-cons(ax2, ndx1, gstore3, jro0), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2[ndx2.keys, ax3]), refsize-cons(gstore2, range fi2), refsize-cons(gstore3[m3, groupblock(gndx, lax, n1)][m, groupblock(gndx0, lax0, m6 + m1)], range fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]), ri-inj(fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]), ri-inj(fi1), ri-inj(fi2), nd.key ∈ fi2[ndx2.keys, ax3], @(m, m0, m1) ∈ gstore3, nd.key ∈ fi2, m3 ∈ gstore2, m3 ∈ gstore3, m ∈ gstore3[m3, groupblock(gndx, lax, n1)], m ∈ gstore2, pmaxino ≤ jmaxino, pmaxino ≤ jmaxino1, jmaxino1 ≤ jmaxino, jmaxino1 ≤ max(nd.key.ino + 1, jmaxino), pmaxino ≤ max(nd.key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore1, fi2[ndx2.keys, ax3].lebs ⊆ dom gstore2, ndx1.keys.toSet ⊆ dom fi2, fi2.lebs ⊆ dom gstore2, ndx2.keys.toSet ⊆ dom fi2, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3[m3, groupblock(gndx, lax, n1)][m, groupblock(gndx0, lax0, m6 + m1)], jro0) ⊦ jmaxino = 0, jmaxino1 = 0, max(nd.key.ino + 1, jmaxino) = 0, pmaxino = 0, dups(nx), dups(ax3 + ax2), dups(ax3), dups(ax2), m ∈ jro0, @(m, m0, m1) ∈ fi2, @(m, m0, m1) ∈ ax2, @(m, m0, m1) ∈ ax3, nodes-cons(ax2, ndx1, gstore3[m3, groupblock(gndx, lax, n1)][m, groupblock(gndx0, lax0, m6 + m1)], jro0) ∧ (dom fi2 ∪ ndx2.keys.toSet) ++ nd.key = dom fi2

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 13

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