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Proof step 67 from proof fsync-inode-others-unchanged (previous step)

files0[m0] = mkfile(m1, md0, m2, content), icache0[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), m0 ∈ files0, m ∈ icache0, ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ valid-file-inode(icache0[ino].inode, dirs, files0) ;valid-ino(ino, dirs, files0) ∧ valid-inode(icache0[ino].inode, dirs, files0) ) ⊦ m0 = m ∧ (ino ≠ m ∧ ino ∈ files0 → (files0[m, (files0[m].meta:= md).size:= m3] ⊕ icache0)[ino] = (files0 ⊕ icache0)[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
icache0[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files0[m0] = mkfile(m1, md0, m2, content), m ∈ icache0, m0 ∈ files0, ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files0 ∧ icache0[ino0].inode.nlink = files0[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files0) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs ⊃ mkinode (icache0[ino0].inode.ino, dirs[icache0[ino0].inode.ino].meta, true, dirs[icache0[ino0].inode.ino].nlink, dirs[icache0[ino0].inode.ino].nsubdirs, dirs[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files0[icache0[ino0].inode.ino].meta, false, files0[icache0[ino0].inode.ino].nlink, 0, files0[icache0[ino0].inode.ino].size) ) ) ⊦ m0 = m ∧ (ino ≠ m ∧ ino ∈ files0 → (files0[m, (files0[m].meta:= md).size:= m3] ⊕ icache0)[ino] = (files0 ⊕ icache0)[ino])

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (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)