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Proof step 162 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, true, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), ino0 ∈ icache, ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ ino0 = ino, mkfile(m8, md2, m9, content1 ⊕ mkcontent(ino0, pcache)) = mkfile(m8, md2, m9, content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 163:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 164:
files[ino0] = mkfile(m8, md2, m9, content1), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, true, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ ino0 = ino, m8 = m8 ∧ md2 = md2 ∧ m9 = m9 ∧ 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)]), m9, md2, m8, content1 ⊕ mkcontent(ino0, pcache), m9, md2, m8] flags: <all paths>

Additional information

Used terms: content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), m9, md2, m8, content1 ⊕ mkcontent(ino0, pcache), m9, md2, m8