[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 200 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino0] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ mkfile(m2, md0, m3, content0 ⊕ mkcontent(ino0, pcache)) = mkfile(m2, md0, m3, content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])), ino0 ∈ icache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 201:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 202:
files[ino0] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ ino0 ∈ icache, m2 = m2 ∧ md0 = md0 ∧ m3 = m3 ∧ content0 ⊕ mkcontent(ino0, pcache) = content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [content0, m2, md0, m1, content, m0, md, m] → [ content0 ⊕ mkcontent (ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), m3, md0, m2, content0 ⊕ mkcontent(ino0, pcache), m3, md0, m2] flags: <all paths>

Additional information

Used terms: content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), m3, md0, m2, content0 ⊕ mkcontent(ino0, pcache), m3, md0, m2