[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 134 from proof inv-gc (previous step)

# lax = # gndx0, # ax = # referenced-adrs(lax.to-adr(n1), fi2), gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1 < jmaxino0, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore3 \ jro), inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), ri-inj(fi1), ri-inj(fi2), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), ∀ n. n ∈ gstore2 → n ∈ gstore3 ⊦ jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dups(nx1), dups(ax), dups(nx0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), n1 ∈ nx1, n1 ∈ jro0, n1 ∈ gstore3 ∧ ¬ n1 ∈ nx0

User applied rule all left

And obtained the following new goals

Proof step 135:
# ax = # referenced-adrs(lax.to-adr(n1), fi2), # lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, jro1 < jmaxino0, inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3 \ jro), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), n1 ∈ gstore2 → n1 ∈ gstore3 ⊦ jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), dups(nx0), dups(ax), dups(nx1), n1 ∈ jro0, n1 ∈ nx1, n1 ∈ gstore3 ∧ ¬ n1 ∈ nx0

Rule argument

pos: left 42 terms: n1 abort: F discard: T computed: T

Additional information

Used terms: n1