[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 37 from proof inv-remove (previous step)

fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2[nx.last]), inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro), inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2 -- key), ri-inj(fi2), valid-journal-head(nx, gstore2, jro), nx.last ∈ gstore2, key ∈ fi2, m ∈ gstore2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1 ⊦ nx = [], pmaxino = 0, dups(nx), valid-journal-head(nx, gstore2[m, groupblock(gndx, lax, n0)], jro)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ (gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end)
Proof step 39:
gstore2[m] = groupblock(gndx, lax, n0 + m1), fi2[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro), inv(gstore2[nx.last]), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-inj(fi2), ri-inj(fi2 -- key), ri-inj(fi1), valid-journal-head(nx, gstore2, jro), m ∈ gstore2, key ∈ fi2, nx.last ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2 ⊦ nx = [], pmaxino = 0, dups(nx), nx ≠ [] ∧ nx.last ∈ gstore2[m, groupblock(gndx, lax, n0)] ∧ ¬ nx.last ∈ jro ∧ (gstore2[m, groupblock(gndx, lax, n0)][nx.last].gndlist = [] ∨ gstore2[m, groupblock(gndx, lax, n0)][nx.last].gndlist.last.end)

Rule argument

spec: gjournal-base name: valid-journal-head seq: ⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ ( gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end) subst: [ginval, gstore, nx] → [jro, gstore2[m, groupblock(gndx, lax, n0)], nx] flags: <all paths>

Additional information

Used terms: jro, gstore2[m, groupblock(gndx, lax, n0)], nx