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Proof step 173 from proof overwrite-write-page-dirty (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 174:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 175:
files[ino0] = mkfile(m4, md0, m5, content), icache[ino0] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m3)), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ ino ∈ icache, m3 = m3 ∧ md = md ∧ m1 = m1 ∧ content ⊕ mkcontent(ino0, pcache) = content ⊕ 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] → [ content ⊕ mkcontent (ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), m1, md, m3, content ⊕ mkcontent(ino0, pcache), m1, md, m3] flags: <all paths>

Additional information

Used terms: content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), m1, md, m3, content ⊕ mkcontent(ino0, pcache), m1, md, m3