[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 299 from proof overwrite-write-page-clean (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ ino0 = ino, mkfile(m7, md1, m5, content1 ⊕ mkcontent(ino0, pcache)) = mkfile(m7, md1, m5, content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 300:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 301:
files[ino0] = mkfile(m8, md2, m9, content1), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ ino0 = ino, m7 = m7 ∧ md1 = md1 ∧ m5 = m5 ∧ content1 ⊕ mkcontent(ino0, pcache) = content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, 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] → [ content1 ⊕ mkcontent (ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), m5, md1, m7, content1 ⊕ mkcontent(ino0, pcache), m5, md1, m7] flags: <all paths>

Additional information

Used terms: content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), m5, md1, m7, content1 ⊕ mkcontent(ino0, pcache), m5, md1, m7