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Proof step 7 from proof pcache-overwrite-read-page (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 9:
files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ datakey(ino, n) ∈ pcache, m1 = m1 ∧ md0 = md0 ∧ m2 = m2 ∧ content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]) = content0 ⊕ mkcontent(ino0, pcache)

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), m2, md0, m1, content0 ⊕ mkcontent (ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]), m2, md0, m1] flags: <all paths>

Additional information

Used terms: content0 ⊕ mkcontent(ino0, pcache), m2, md0, m1, content0 ⊕ mkcontent (ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]), m2, md0, m1