[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 13 from proof refine-newino (previous step)

remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, p_os.keys.inodes?, jro.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-inj(fi1), ri-inj(ri), jmaxino ∈ p_os, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid → jvalid0 ⊦ # p_os = 0, jmaxino = 0, p_os = ∅, pmaxino = 0, dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ns < n ↔ (∀ n0. n0 ∈ ns → n0 < n)
Proof step 15:
remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jro.keys.inodes?, p_os.keys.inodes?, jro < jmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), ri-inj(ri), ri-inj(fi1), jmaxino ∈ p_os, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), ∀ n0. n0 ∈ p_os → n0 < pmaxino ⊦ # p_os = 0, jmaxino = 0, p_os = ∅, pmaxino = 0, dups(nx)

Rule argument

spec: oset, inst: nat-set name: Greater seq: ⊦ ns < n ↔ (∀ n0. n0 ∈ ns → n0 < n) subst: [n, ns] → [pmaxino, p_os] flags: <all paths>

Additional information

Used terms: pmaxino, p_os