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Proof step 82 from proof inv-store (previous step)

gstore3[m3] = groupblock(gndx, lax, n1 + m5), fi2[key] = @(m3, m4, m5), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), gstore3[m3, groupblock(gndx, lax, n1)][m0] = groupblock(gndx0, lax0, m6), 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(gstore3[m3, groupblock(gndx, lax, n1)] \ jro0), inv(gstore2), inv(gstore3 \ jro0), inv(gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + 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 ∈ gstore3[m3, groupblock(gndx, lax, n1)], @(m0, m1, m2) ∈ gstore3, key ∈ fi2, m3 ∈ gstore3, m0 ∈ dom gstore3 ∪ jro0, pmaxino ≤ jmaxino, pmaxino ≤ max(key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3 ⊦ #(dom gstore3 ∪ jro0) = 0, jmaxino = 0, max(key.ino + 1, jmaxino) = 0, nx = [], pmaxino = 0, dom gstore3 ∪ jro0 = ∅, dups(nx), @(m0, m1, m2) ∈ fi2, nx ≠ [] ∧ nx.last ∈ gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)] ∧ ¬ nx.last ∈ jro0 ∧ ( gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)][nx.last].gndlist = [] ∨ gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)][nx.last].gndlist.last.end)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
gstore3[m3] = groupblock(gndx, lax, n1 + m5), fi2[key] = @(m3, m4, m5), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), gstore3[m3, groupblock(gndx, lax, n1)][m0] = groupblock(gndx0, lax0, m6), 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(gstore3[m3, groupblock(gndx, lax, n1)] \ jro0), inv(gstore2), inv(gstore3 \ jro0), inv(gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + 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 ∈ gstore3[m3, groupblock(gndx, lax, n1)], @(m0, m1, m2) ∈ gstore3, key ∈ fi2, m3 ∈ gstore3, m0 ∈ dom gstore3 ∪ jro0, nx.last ∈ gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)], pmaxino ≤ jmaxino, pmaxino ≤ max(key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3 ⊦ #(dom gstore3 ∪ jro0) = 0, gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)][nx.last].gndlist = [], jmaxino = 0, max(key.ino + 1, jmaxino) = 0, nx = [], pmaxino = 0, dom gstore3 ∪ jro0 = ∅, gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)][nx.last].gndlist.last.end, dups(nx), @(m0, m1, m2) ∈ fi2

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore; (ws)% ⊦ elems nx ∩ ginval = ∅ ∧ nx ≠ [] → ¬ nx.last ∈ ginval; (s)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]