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Proof step 111 from proof fsync-inode-keep-abs (previous step)

icache[m] = mkientry(true, inode), err = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, icache-cons(icache, dirs, files), pre-write-inode(inode, dirs, files), m ∈ icache ⊦ [fail#(; ; err); asynced := ?; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (files0 = (files ⊕ pcache) ⊕ icache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 112:
icache[m] = mkientry(true, inode), icache-cons(icache, dirs, files), m ∈ icache, inode.ino ∈ dirs ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory ∨ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory ⊦ [fail#(; ; err); asynced := ?; files0 := (files ⊕ pcache) ⊕ icache; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (files0 = (files ⊕ pcache) ⊕ icache)

Rule argument

Additional information

Used simplifier rules: ⊦ 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)