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Proof step 83 from proof overwrite-write-page-dirty (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 84:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 85:
files[ino0] = mkfile(m6, md1, m7, content0), icache[ino0] = mkientry(boolvar, mkinode(m2, md0, true, m3, m4, m5)), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ ino0 = ino, m6 = m6 ∧ md1 = md1 ∧ m7 = m7 ∧ 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)]), m7, md1, m6, content0 ⊕ mkcontent(ino0, pcache), m7, md1, m6] flags: <all paths>

Additional information

Used terms: content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), m7, md1, m6, content0 ⊕ mkcontent(ino0, pcache), m7, md1, m6