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Proof step 688 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ files, ino ∈ files ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]);((files ⊕ pcache) ⊕ icache)[ino0]) = ((files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache)[ino0], ino0 ∈ icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 689:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files, ino0 ∈ files ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]) ;mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)) ) = mkfile ((ino0 = ino ⊃ mkfile(m2, md0, m3, content0[m, buf]);files[ino0]).size, (ino0 = ino ⊃ mkfile(m2, md0, m3, content0[m, buf]);files[ino0]).meta, (ino0 = ino ⊃ mkfile(m2, md0, m3, content0[m, buf]);files[ino0]).nlink, (ino0 = ino ⊃ mkfile(m2, md0, m3, content0[m, buf]);files[ino0]).content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])), ino0 ∈ icache

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite-not-cached: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino];%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)