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Proof step 2 from proof fsync-pages-overwrite (previous step)

files = files0, pcache0 = pcache, afs-cons(dirs, files), pcache-cons(pcache, dirs, files), valid-file-inode(inode, dirs, files) ⊦ [cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)] (err = ESUCCESS → files[inode.ino].trunc(inode.size) = (files0 ⊕ pcache0)[inode.ino].trunc(inode.size))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
inode.nlink = files0[inode.ino].nlink, inode.nsubdirs = 0, files = files0, pcache0 = pcache, afs-cons(dirs, files0), pcache-cons(pcache, dirs, files0), inode.ino ∈ files0, ¬ inode.directory ⊦ [cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)] ( err = ESUCCESS → files[inode.ino].content:= (files[inode.ino].content upto inode.size) = mkfile (files0[inode.ino].size, files0[inode.ino].meta, files0[inode.ino].nlink, (files0[inode.ino].content ⊕ mkcontent(inode.ino, pcache0)) upto inode.size))

Rule argument

Additional information

Used simplifier rules: trunc-def: ⊦ af.trunc(n) = af.content:= (af.content upto n);%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)