[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 42 from proof refine-remove (previous step)

gstore2[m] = groupblock(gndx, lax, n0 + m1), ri[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-inj(fi1), ri-inj(ri -- key), ri-inj(ri), key ∈ ri, m ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]), jmaxino = 0, pmaxino = 0, dups(nx), ∀ n. (n ∈ gstore2 ↓ ↔ n ∈ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]) ∧ ( n ∈ gstore2 ↓ → gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n].gndlist = gstore2 ↓[n].gndlist ∧ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n].ladrlist = gstore2 ↓[n].ladrlist)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
ri[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro0), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-inj(ri), ri-inj(ri -- key), ri-inj(fi1), m ∈ gstore2, key ∈ ri, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]), jmaxino = 0, pmaxino = 0, dups(nx), (n ∈ gstore2 → n ∈ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]) ∧ ( n ∈ gstore2 → gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n].gndlist = gstore2[n] ↓.gndlist ∧ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n].ladrlist = gstore2[n] ↓.ladrlist)

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)% ⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore; (ws)% ⊦ n ∈ gstore ↓ ↔ n ∈ gstore; (s)