[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 31 from proof initialization (previous step)

fi0 = ∅ ⊦ ⟪aubifs_core_index_store#(inodekey(ROOT_INO), adr1, ∅, ∅, ∅, (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], adr1 ', boolvar; fi0); ro := ∅; fs := (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)]; err := ESUCCESS; if err = ESUCCESS then aubifs_core_journal_sync#(fi0, ∅, ro, ∅, fs, adr1 '; ; boolvar, err)⟫ ( ( err = ESUCCESS → ⟨afs_format#(n, boolvar0, LEB_SIZE, md; dirs0; files0, asynced, err1)⟩ ( dirs0 = abs-dirs(fs, fi0) ∧ files0 = abs-files(fs, fi0) ∧ orphans(abs-dirs(fs, fi0), abs-files(fs, fi0)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ ESUCCESS = err1)) ∧ ( err ≠ ESUCCESS → (∀ dirs, files, boolvar. ⟨afs_format#(n, boolvar0, LEB_SIZE, md; dirs0; files0, asynced, err1)⟩ (dirs = dirs0 ∧ files = files0 ∧ (boolvar ↔ asynced) ∧ err = err1))))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 32:
adr = adr1, fi = ∅, fi0 = ∅, fo = ∅, fs = (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], key = inodekey(ROOT_INO), log = adr1 ', ri = fi0, ro = ∅ ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; ro := ∅; fs := (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)]; err := ESUCCESS; fi0 := ri; if err = ESUCCESS then aubifs_core_journal_sync#(fi0, ∅, ro, ∅, fs, adr1 '; ; boolvar, err)⟫ ( ( err = ESUCCESS → ⟨afs_format#(n, boolvar0, LEB_SIZE, md; dirs0; files0, asynced, err1)⟩ ( dirs0 = abs-dirs(fs, fi0) ∧ files0 = abs-files(fs, fi0) ∧ orphans(abs-dirs(fs, fi0), abs-files(fs, fi0)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ ESUCCESS = err1)) ∧ ( err ≠ ESUCCESS → (∀ dirs, files, boolvar. ⟨afs_format#(n, boolvar0, LEB_SIZE, md; dirs0; files0, asynced, err1)⟩ (dirs = dirs0 ∧ files = files0 ∧ (boolvar ↔ asynced) ∧ err = err1))))

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_index_store#(KEY, ADR, FI, RO, FO, FS, LOG, CSYNCED; RI) {if ¬ ADR ∈ RI ∧ ADR ∈ FS ∧ key-cons(KEY, FS[ADR]) then RI[KEY] := ADR else abort };