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Proof step 14 from proof pcache-overwrite-read-page (previous step)

files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]) ↔ n0 ∈ content0 ⊕ mkcontent(ino0, pcache), datakey(ino, n) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1
Proof step 16:
files[ino] = mkfile(m, md, m0, content), files[ino0] = mkfile(m1, md0, m2, content0), ino0 ∈ files, ino ∈ files, n ∈ content ⊦ n0 ∈ content0 ∨ n0 ∈ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]) ↔ n0 ∈ content0 ⊕ mkcontent(ino0, pcache), datakey(ino, n) ∈ pcache

Rule argument

spec: <toplevel> name: in-overwrite-content seq: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1 subst: [content1, content0, n] → [mkcontent (ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]), content0, n0] flags: <all paths>

Additional information

Used terms: mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]), content0, n0