[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 101 from proof refine-gc (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: gjournal-base name: referenced-adrs-lookup-keys-nodups seq: ⊦ ri-cons(ri, fs) ∧ ¬ dups(ax) → ¬ dups(fs[referenced-adrs(ax, ri)].keys) subst: [ri, ax, fs] → [ri, lax.to-adr(n1), nodes(gstore2 ↓, jro0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ dups(lax.to-adr(n)) ↔ dups(lax); (s)% ⊦ inv(groupblock(gndx, lax, m0)) → ¬ dups(lax); (s) Used terms: ri, lax.to-adr(n1), nodes(gstore2 ↓, jro0)