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Proof step 61 from proof fsync-inode-keep-abs (previous step)

icache[m] = mkientry(true, inode), err = ESUCCESS, err0 = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, icache-cons(icache, dirs, files), pre-write-inode(inode, dirs, files), m ∈ icache ⊦ [icache_set_status#(m, false; err, icache)] ( files0 = ( files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ] ⊕ pcache) ⊕ icache), inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
inode.nlink = files[inode.ino].nlink, inode.nsubdirs = 0, icache[m] = mkientry(true, inode), err = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, icache-cons(icache, dirs, files), m ∈ icache, inode.ino ∈ files, ¬ inode.directory ⊦ [icache_set_status#(m, false; err, icache)] (files0 = (files[inode.ino, (files[inode.ino].meta:= inode.meta).size:= inode.size] ⊕ pcache) ⊕ icache)

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (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)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)