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Proof step 73 from proof fsync-inode-overwrite (previous step)

files0[m2] = mkfile(m3, md1, m4, content0), icache[m] = mkientry(true, mkinode(m2, md, false, m4, 0, m5)), files0[m] = mkfile(m0, md0, m1, content), m ∈ files0, m2 ∈ files0, m ∈ icache, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files0 ∧ icache[ino].inode.nlink = files0[icache[ino].inode.ino].nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[ino].inode = (icache[ino].inode.ino ∈ dirs ⊃ mkinode (icache[ino].inode.ino, dirs[icache[ino].inode.ino].meta, true, dirs[icache[ino].inode.ino].nlink, dirs[icache[ino].inode.ino].nsubdirs, dirs[icache[ino].inode.ino].size) ;mkinode (icache[ino].inode.ino, files0[icache[ino].inode.ino].meta, false, files0[icache[ino].inode.ino].nlink, 0, files0[icache[ino].inode.ino].size) ) ) ⊦ mkfile(m5, md, m4, content0) = (files0 ⊕ icache)[m2]

User applied rule all left

And obtained the following new goals

Proof step 74:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m2, md, false, m4, 0, m5)), files0[m2] = mkfile(m3, md1, m4, content0), m ∈ icache, m2 ∈ files0, m ∈ files0, m ∈ icache → icache[m].inode.ino = m ∧ (icache[m].dirty ⊃ icache[m].inode.ino ∈ files0 ∧ icache[m].inode.nlink = files0[icache[m].inode.ino].nlink ∧ icache[m].inode.nsubdirs = 0 ∧ ¬ icache[m].inode.directory ; (m ∈ dirs ∨ m ∈ files0) ∧ icache[m].inode = (icache[m].inode.ino ∈ dirs ⊃ mkinode (icache[m].inode.ino, dirs[icache[m].inode.ino].meta, true, dirs[icache[m].inode.ino].nlink, dirs[icache[m].inode.ino].nsubdirs, dirs[icache[m].inode.ino].size) ;mkinode (icache[m].inode.ino, files0[icache[m].inode.ino].meta, false, files0[icache[m].inode.ino].nlink, 0, files0[icache[m].inode.ino].size) ) ), ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files0 ∧ icache[ino].inode.nlink = files0[icache[ino].inode.ino].nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[ino].inode = (icache[ino].inode.ino ∈ dirs ⊃ mkinode (icache[ino].inode.ino, dirs[icache[ino].inode.ino].meta, true, dirs[icache[ino].inode.ino].nlink, dirs[icache[ino].inode.ino].nsubdirs, dirs[icache[ino].inode.ino].size) ;mkinode (icache[ino].inode.ino, files0[icache[ino].inode.ino].meta, false, files0[icache[ino].inode.ino].nlink, 0, files0[icache[ino].inode.ino].size) ) ) ⊦ mkfile(m5, md, m4, content0) = (files0 ⊕ icache)[m2]

Rule argument

pos: left 7 terms: m abort: F discard: F computed: T

Additional information

Used terms: m