[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 51 from proof inv-truncate (previous step)

gstore2[m] = groupblock(gndx, lax, n1 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, p_os < pmaxino, fi1.inos < jmaxino, fi2.inos < pmaxino, gstore2 =○refsize gstore3, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro), inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), refsize-cons(gstore3, range fi1), refsize-cons(gstore1, range fi2), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi2), @(m, m0, m1) ∈ as0, m ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, as0.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ # as0 = 0, as0 = ∅, pmaxino = 0, dups(nx), ∀ n. n ∈ gstore2[m, groupblock(gndx, lax, n1)] → gstore2[m, groupblock(gndx, lax, n1)][n].ref-size = ((range(fi1 \ datakeys(key, n0, fi1)) ∪ (as0 -- @(m, m0, m1))) | n).size

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
gstore2[m] = groupblock(gndx, lax, n1 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), n ∈ gstore2[m, groupblock(gndx, lax, n1)], m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ # as0 = 0, gstore2[m, groupblock(gndx, lax, n1)][n].ref-size = ((range(fi1 \ datakeys(key, n0, fi1)) | n) ∪ ((as0 -- @(m, m0, m1)) | n)).size, as0 = ∅, pmaxino = 0, dups(nx)

Rule argument

Additional information

Used simplifier rules: unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ (as0 ∪ as1) | n = (as0 | n) ∪ (as1 | n); (s)