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Proof step 69 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, m ∈ icache0 → icache0[m].inode.ino = m ∧ (icache0[m].dirty ⊃ icache0[m].inode.ino ∈ files0 ∧ icache0[m].inode.nlink = files0[icache0[m].inode.ino].nlink ∧ icache0[m].inode.nsubdirs = 0 ∧ ¬ icache0[m].inode.directory ; (m ∈ dirs ∨ m ∈ files0) ∧ icache0[m].inode = (icache0[m].inode.ino ∈ dirs ⊃ mkinode (icache0[m].inode.ino, dirs[icache0[m].inode.ino].meta, true, dirs[icache0[m].inode.ino].nlink, dirs[icache0[m].inode.ino].nsubdirs, dirs[icache0[m].inode.ino].size) ;mkinode (icache0[m].inode.ino, files0[icache0[m].inode.ino].meta, false, files0[icache0[m].inode.ino].nlink, 0, files0[icache0[m].inode.ino].size) ) ), ∀ 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
icache0[m0] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files0[m0] = mkfile(m1, md0, m2, content), ino ∈ files0, m0 ∈ 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) ) ) ⊦ (files0[m0, mkfile(m3, md, m2, content)] ⊕ icache0)[ino] = (files0 ⊕ icache0)[ino], ino = m0

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)