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Proof step 19 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 ⊦ (content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]))[n0] = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino, n) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 21:
files[ino] = mkfile(m, md, m0, content), files[ino0] = mkfile(m1, md0, m2, content0), ino0 ∈ files, ino ∈ files, n ∈ content ⊦ (content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]))[n0] = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino, n) ∈ pcache, n0 ∈ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])])
Proof step 24:
files[ino] = mkfile(m, md, m0, content), files[ino0] = mkfile(m1, md0, m2, content0), ino0 ∈ files, ino ∈ files, n ∈ content, n0 ∈ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]) ⊦ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])])[n0] = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino, n) ∈ pcache

Rule argument

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

Additional information

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