[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 21 from proof abs-files-new (previous step)

files[ino0] = mkfile(m, md0, m0, content), (files ++ ino)[ino0] = mkfile(m1, md, m2, content0), ino0 ∈ files ⊦ ino = 0, mkfile(md0, (content.stream to m).buf) = mkfile(md, (content0.stream to m1).buf), ino ∈ files

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino]

Rule argument

spec: heap, inst: file-heap name: at-alloc seq: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino] subst: [ino, ino0, files] → [ino0, ino, files] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used terms: ino0, ino, files