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Proof step 86 from proof fsync-inode-others-unchanged (previous step)

dirs[m0] = mkdir(m6, md1, m7, m8, entries), icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), files0[m0] = mkfile(m4, md0, m5, content), m ∈ icache0, ⌊err0⌋ , ∀ 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 ∈ dirs ∧ m1 = m7 ∧ m3 = m6 ∧ m2 = m8 ∧ boolvar ∨ m0 ∈ files0 ∧ m1 = m5 ∧ m2 = 0 ∧ ¬ boolvar ⊦ m0 = m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
files0[m0] = mkfile(m4, md0, m5, content), icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), dirs[m0] = mkdir(m6, md1, m7, m8, entries), m ∈ icache0, ⌊err0⌋ , ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ icache0[ino].inode.ino ∈ files0 ∧ icache0[ino].inode.nlink = files0[icache0[ino].inode.ino].nlink ∧ icache0[ino].inode.nsubdirs = 0 ∧ ¬ icache0[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache0[ino].inode = (icache0[ino].inode.ino ∈ dirs ⊃ mkinode (icache0[ino].inode.ino, dirs[icache0[ino].inode.ino].meta, true, dirs[icache0[ino].inode.ino].nlink, dirs[icache0[ino].inode.ino].nsubdirs, dirs[icache0[ino].inode.ino].size) ;mkinode (icache0[ino].inode.ino, files0[icache0[ino].inode.ino].meta, false, files0[icache0[ino].inode.ino].nlink, 0, files0[icache0[ino].inode.ino].size) ) ), m0 ∈ dirs ∧ m1 = m7 ∧ m3 = m6 ∧ m2 = m8 ∧ boolvar ∨ m0 ∈ files0 ∧ m1 = m5 ∧ m2 = 0 ∧ ¬ boolvar ⊦ m0 = m

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)