[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 17 from proof inv-truncate (previous step)

jvalid0 ↔ jvalid2, as = as0, as1 = fi1[datakeys(key, n0, fi1)], dom gstore = dom gstore4, fi = fi2, fi0 = fi1 \ datakeys(key, n0, fi1), gstore0 = gstore1, gstore2 = gstore3, gstore4 = gstore3, remove-refsize0(gstore1) = gstore1, as ∩ range fi0 = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore =○refsize gstore4, inv(gstore1), inv(gstore3 \ jro), inv-journal(nx, gstore, gstore0, jro), refsize-cons(gstore, range fi0 ∪ as), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), adr ∈ as, pmaxino ≤ jmaxino, as.lebs ⊆ dom gstore, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid0 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ ⟪index_get_gblock_refsize#(adr.lnum, fi0, fi, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi0, fi, jro, gstore0, nx, pmaxino, p_os, jvalid; gstore); as := as -- adr⟫ ( ( (jvalid0 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ dom gstore = dom gstore4 ∧ as ∩ range fi0 = ∅ ∧ as.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi0 ∪ as) ∧ inv-journal(nx, gstore, gstore0, jro) ∧ gstore =○refsize gstore4) ∧ # as < # as0), as = ∅, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
dom gstore = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, # as0 ≠ 0, as0 ≠ ∅, pmaxino ≠ 0, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore =○refsize gstore3, inv(gstore \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), adr ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, ¬ dups(nx), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ ⟪index_get_gblock_refsize#(adr.lnum, fi1 \ datakeys(key, n0, fi1), fi2, jro, gstore, gstore1, nx, pmaxino, p_os, jvalid; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi1 \ datakeys(key, n0, fi1), fi2, jro, gstore1, nx, pmaxino, p_os, jvalid; gstore); as := as0 -- adr⟫ ( (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ dom gstore = dom gstore3 ∧ as ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅ ∧ as.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range(fi1 \ datakeys(key, n0, fi1)) ∪ as) ∧ inv(gstore \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore ∪ jro ∧ gstore =○refsize gstore3 ∧ # as < # as0)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)