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Proof step 65 from proof inv-gc-update-index (previous step)

# ax3 = # ndx2, # ax2 = # ndx1, jvalid ↔ jvalid0, 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, fi = fi1, fi0 = fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)], gstore = gstore3[m3, groupblock(gndx, lax, n1)], gstore0 = gstore1, jro = jro0, lnum = m, n = m6 + m1, 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 gstore[lnum, gstore[lnum].ref-size:= n] ∪ jro0, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, fi2[ndx2.keys, ax3].inos < max(nd.key.ino + 1, jmaxino), 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, gstore[lnum, gstore[lnum].ref-size:= n] =○refsize gstore3, inv(gstore[lnum, gstore[lnum].ref-size:= n] \ 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(gstore[lnum, gstore[lnum].ref-size:= n], range fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2[ndx2.keys, ax3]), refsize-cons(gstore2, range fi2), ri-inj(fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]), ri-inj(fi1), ri-inj(fi2), m ∈ gstore3[m3, groupblock(gndx, lax, n1)], nd.key ∈ fi2[ndx2.keys, ax3], @(m, m0, m1) ∈ gstore3, nd.key ∈ fi2, m3 ∈ gstore2, m3 ∈ gstore3, lnum ∈ gstore, pmaxino ≤ max(nd.key.ino + 1, jmaxino), pmaxino ≤ jmaxino, pmaxino ≤ jmaxino1, jmaxino1 ≤ jmaxino, fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)].lebs ⊆ dom gstore[lnum, gstore[lnum].ref-size:= n], 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, gstore[lnum, gstore[lnum].ref-size:= n], jro0), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, 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, (∃ ax, ndx. # ax = # ndx ∧ ax3 + @(m, m0, m1) ' + ax2 = ax + ax2 ∧ ndx2 + nd ' + ndx1 = ndx + ndx1 ∧ fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)] = fi2[ndx.keys, ax]) ∧ (dom fi2 ∪ ndx2.keys.toSet) ++ nd.key = dom fi2 ∧ jmaxino1 ≤ max(nd.key.ino + 1, jmaxino) ∧ dom gstore[lnum, gstore[lnum].ref-size:= n] = dom gstore2 ∧ nodes-cons(ax2, ndx1, gstore[lnum, gstore[lnum].ref-size:= n], jro0) ∧ (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore[lnum, gstore[lnum].ref-size:= n], jro0)) ∧ ¬ # ax2 < # ax2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ ¬ max(n, m) < m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ groupblock(gndx, lax, m).ref-size:= m0 = groupblock(gndx, lax, m0); (s)%⊦ ri.lebs ⊆ dom gstore ∧ m ∈ gstore → ri[key, @(m, m1, m2)].lebs ⊆ dom gstore; (s)% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ ¬ n ∈ ns → (n ∈ ns ∪ ns0 ↔ n ∈ ns0); (s)% ⊦ ns ++ n = ns ↔ n ∈ ns; (s)% ⊦ ¬ n < n; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # nd ' = 0 +1; (s)% ⊦ #(ndx + ndx0) = # ndx + # ndx0; (s)% ⊦ # adr ' = 0 +1; (s)% ⊦ #(ax + ax0) = # ax + # ax0; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]%# kx = # ax ⊦ ri[kx + key ', ax + adr '] = ri[kx, ax][key, adr]; (s)% ⊦ # ndx.keys = # ndx; (s)% ⊦ nd '.keys = nd.key '; (s)% ⊦ (ndx0 + ndx1).keys = ndx0.keys + ndx1.keys; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ ndx + ndx0 = ndx1 + ndx0 ↔ ndx = ndx1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + ax0 = ax1 + ax0 ↔ ax = ax1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ns < n → ns < max(m + 1, n); (s)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ (ns ++ n) ∪ ns0 = (ns ∪ ns0) ++ n; (s)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)