[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 3 from proof inv-truncate (previous step)

gstore1 = gstore, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, pmaxino ≠ 0, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro), inv(gstore0), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), ri-inj(fi), ri-inj(fi0), pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪gjournal_index_truncate#(key, n, jvalid, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; fi, gstore)⟫ ( fi.inos < jmaxino ∧ (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro ∧ ri-inj(fi) ∧ gstore =○refsize gstore1)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
jvalid0 ↔ jvalid2, jvalid ↔ jvalid1, gstore1 = gstore, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, inv(gstore0), inv(gstore \ jro), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-inj(fi0), ri-inj(fi), pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪let as = ? in {index_index_truncate#(key, n, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid; as, fi); gjournal_remove_addresses#(jvalid0, fi, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid; as, gstore)}⟫ ( fi.inos < jmaxino ∧ (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro ∧ ri-inj(fi) ∧ gstore =○refsize gstore1), pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: truncate: ⊦ ;