[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-contains (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟨aubifs_core_index_contains#(key, ri, fi1, jro1.keys, p_os.keys, nodes(gstore2 ↓, jro0), abs-log(nx, gstore2 ↓), jvalid4; jvalid3; err1)⟩ ((jvalid4 → jvalid0) ∧ (key ∈ ri ↔ jvalid3) ∧ ESUCCESS = err1)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 14:
jvalid0 ↔ jvalid4, jvalid ↔ jvalid3, fi = fi1, fo = p_os.keys, fs = nodes(gstore2 ↓, jro0), log = abs-log(nx, gstore2 ↓), remove-refsize0(gstore1) = gstore1, ro = jro1.keys, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid4 → jvalid2 ⊦ ⟨fail_or_success#(; ; err); if err = ESUCCESS then jvalid := key ∈ ri else jvalid := ?⟩ ((jvalid4 → jvalid2) ∧ (key ∈ ri ↔ jvalid) ∧ ESUCCESS = err), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_index_contains# (KEY, RI, FI, RO, FO, FS, LOG, CSYNCED; EXISTS; ERR) {fail_or_success#(; ; ERR); if ERR = ESUCCESS then EXISTS := KEY ∈ RI else EXISTS := ? };