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Proof step 77 from proof fsync-inode-overwrite (previous step)

files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), err = ESUCCESS, files = files0, inode = inode1, icache-cons(icache, dirs, files0), pre-write-inode(inode, dirs, files), m ∈ icache, m ∈ files0 ⊦ [fail#(; ; err); asynced := ?; icache0 := icache; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → files[inode.ino] = (files0 ⊕ icache0)[inode.ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache, inode1.ino ∈ dirs ∧ inode1.nlink = dirs[inode1.ino].nlink ∧ inode1.size = dirs[inode1.ino].size ∧ inode1.nsubdirs = dirs[inode1.ino].nsubdirs ∧ inode1.directory ∨ inode1.ino ∈ files0 ∧ inode1.nlink = files0[inode1.ino].nlink ∧ inode1.nsubdirs = 0 ∧ ¬ inode1.directory ⊦ [fail#(; ; err); asynced := ?; icache0 := icache; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → files0[inode.ino] = (files0 ⊕ icache0)[inode.ino])

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)