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Proof step 174 from proof inv-addn (previous step)

# lax0 = # gndx0, # lax = # gndx, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore0) = gstore0, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(groupblock(gndx0, lax0, m0)), inv(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv(gstore0), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv-flashsize(gndx, lax), refsize-cons(gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], range fi2), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore0, dom gstore2 ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ gndx = [], nx0 = [], pmaxino = 0, dups(nx1), dups(nx0), dups(lax), nx0 ≠ [] ∧ nx0.last ∈ gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)] ∧ ¬ nx0.last ∈ jro0 ∧ ( gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)][nx0.last].gndlist = [] ∨ gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)][nx0.last].gndlist.last.end)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 175:
# lax = # gndx, # lax0 = # gndx0, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore0), inv(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv(groupblock(gndx0, lax0, m0)), inv-flashsize(gndx, lax), refsize-cons(gstore3, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore2, range fi2), refsize-cons(gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], range fi2), ri-inj(fi1), ri-inj(fi2), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, dom gstore2 ⊆ dom gstore3, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ gndx0 + gndx = [], gndx = [], nx0 = [], pmaxino = 0, gndx.last.end, dups(lax), dups(nx0), dups(nx1)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx ≠ [] → (gndx0 + gndx).last = gndx.last; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ 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]% ⊦ n ∈ gstore[n, gblock]; (s)