[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 49 from proof recovery (previous step)

fs[⌜ino0⌝ ] = mkfile(files1[ino0].meta, (files1[ino0].content.stream to files1[ino0].size).buf), tree0.dir?, dom of1 < ino, abs(tree0, ROOT_INO)(dirs0), afs-cons(dirs0, files1 \ orphans(dirs0, files1)), afs-cons(dirs0, files1), fids-cons(tree0, abs-files(files1), abs-of(of1)), of-cons(∅, dirs0, files1 \ orphans(dirs0, files1)), of-cons(of1, dirs0, files1), ino0 ∈ files1, ⌜ino0⌝ ∈ fs, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files1 ⊦ # links(ino0, dirs0) = 0, links(ino0, dirs0) = ∅, mkfile(files1[ino0].meta, (files1[ino0].content.stream to files1[ino0].size).buf) = abs-files(files1 \ orphans(dirs0, files1))[⌜ino0⌝ ]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
fs[⌜ino0⌝ ] = mkfile(md, (content.stream to m).buf), files1[ino0] = mkfile(m, md, m0, content), tree0.dir?, dom of1 < ino, abs(tree0, ROOT_INO)(dirs0), afs-cons(dirs0, files1), afs-cons(dirs0, files1 \ orphans(dirs0, files1)), fids-cons(tree0, abs-files(files1), abs-of(of1)), of-cons(of1, dirs0, files1), of-cons(∅, dirs0, files1 \ orphans(dirs0, files1)), ⌜ino0⌝ ∈ fs, ino0 ∈ files1, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files1 ⊦ # links(ino0, dirs0) = 0, links(ino0, dirs0) = ∅, mkfile(md, (content.stream to m).buf) = abs-files(files1 \ orphans(dirs0, files1))[⌜ino0⌝ ]

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files1[ino0], m, md, m0, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files1[ino0], m, md, m0, content