[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 4 from proof inv-lookup (previous step)

jvalid ↔ jvalid1, fi = fi1, fi0 = fi2, gstore = gstore1, gstore0 = gstore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro)), ri-inj(fi1), ri-inj(fi2), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪if ri-cons(fi0, nodes(gstore0 ↓, jro)) then let adr = ? in {index_index_lookup#(key, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; jvalid, adr; err); if err = ESUCCESS ∧ jvalid then let gnd = ? in {index_read_gnd#(adr, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; gnd; err); if err = ESUCCESS then nd := gnd.nd}} else abort⟫ true, pmaxino = 0, dups(nx)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 5:
jvalid ↔ jvalid1, fi = fi1, fi0 = fi2, gstore = gstore1, gstore0 = gstore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro)), ri-inj(fi2), ri-inj(fi1), pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪let adr = ? in {index_index_lookup#(key, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; jvalid, adr; err); if err = ESUCCESS ∧ jvalid then let gnd = ? in {index_read_gnd#(adr, fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os, jvalid0; gnd; err); if err = ESUCCESS then nd := gnd.nd}}⟫ true, pmaxino = 0, dups(nx)

Rule argument

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) → ( ri-cons(ri0, fs0) ↔ (∀ key. (key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) → key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]]))); (ss)