[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 213 from proof refine-gc (previous step)

# gstore2[n1].ladrlist = # gndx0, # ax0 = # referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0), gstore2[n1] = groupblock(gndx0, gstore2[n1].ladrlist, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx0 = jro ∪ dom gstore3, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, ri0.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys, ax0].inos < jmaxino0, jro1 < jmaxino0, inv(gstore2 \ jro0), inv(gstore1), inv(gstore2[n1]), inv(gstore3 \ jro), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro0)), new(ax0, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3 -- n1, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri0), refsize-cons(gstore3, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), ri-cons(ri0, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys, ax0]), ri-inj(ri0), n1 ∈ jro ∪ dom gstore3, n1 ∈ gstore3, n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, range ri0 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, ri0.lebs ⊆ dom gstore2, dom gstore2 ⊆ dom gstore3, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys, ax0].lebs ⊆ dom gstore3, ri0.lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid5 → jvalid4 ⊦ #((dom nodes(gstore3 ↓, jro) | n1) ∩ ax0.toSet) = 0, #(jro ∪ dom gstore3) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, (dom nodes(gstore3 ↓, jro) | n1) ∩ ax0.toSet = ∅, jro ∪ dom gstore3 = ∅, dups(nx1), dups(nx0), dups(ax0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys), n1 ∈ nx1, n1 ∈ nx0, n1 ∈ jro0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 214:
# ax0 = # referenced-adrs(lax.to-adr(n1), ri0), # lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), gstore2[n1] = groupblock(gndx, lax, m), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)]], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = jro ∪ dom gstore3, p_os.keys.inodes?, jro1.keys.inodes?, jro1 < jmaxino0, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0].inos < jmaxino0, jro1 < jmaxino, p_os < pmaxino, ri0.inos < jmaxino, fi1.inos < pmaxino, inv(gstore3 \ jro), inv(gstore2[n1]), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro0)), new(ax0, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), refsize-cons(gstore2, range ri0), refsize-cons(gstore1, range fi1), refsize-cons(gstore3 -- n1, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), ri-cons(ri0, nodes(gstore2 ↓, jro0)), ri-inj(ri0), ri-inj(ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0]), ri-inj(fi1), n1 ∈ gstore2, n1 ∈ gstore1, n1 ∈ gstore3, n1 ∈ jro ∪ dom gstore3, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, ri0.lebs ⊆ dom gstore3, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0].lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, ri0.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range ri0 ⊆ dom nodes(gstore2 ↓, jro0), jvalid5 → jvalid4, jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1) ⊦ #(jro ∪ dom gstore3) = 0, #((dom nodes(gstore3 ↓, jro) | n1) ∩ ax0.toSet) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, (dom nodes(gstore3 ↓, jro) | n1) ∩ ax0.toSet = ∅, jro ∪ dom gstore3 = ∅, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys), dups(ax0), dups(nx0), dups(nx1), n1 ∈ jro0, n1 ∈ nx0, n1 ∈ nx1

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore2[n1], gndx, lax, m]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2[n1], gndx, lax, m