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Proof step 58 from proof fsync-inode-overwrite (previous step)

files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), err = ESUCCESS, err0 = ESUCCESS, files = files0, icache0 = icache, inode = inode1, icache-cons(icache, dirs, files0), pre-write-inode(inode, dirs, files), m ∈ icache, m ∈ files0 ⊦ [inode0 := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] ( err = ESUCCESS → 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 ] [inode0.ino ] = (files0 ⊕ icache0)[inode0.ino]), inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
inode1.nlink = files0[inode1.ino].nlink, inode1.nsubdirs = 0, icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, icache0 = icache, icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache, inode1.ino ∈ files0, ¬ inode1.directory ⊦ [inode0 := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] ( err = ESUCCESS → (inode0.ino = inode1.ino ⊃ (files0[inode1.ino].meta:= inode1.meta).size:= inode1.size;files0[inode0.ino]) = (files0 ⊕ icache0)[inode0.ino])

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)