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Proof step 86 from proof fsync-inode-keep-abs (previous step)

icache[ino] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[m0] = mkfile(m1, md0, m2, content), ino ∈ files, m0 ∈ files, m ∈ icache, ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache)[ino], ino = m, ino ∈ icache ∧ ¬ boolvar

User applied rule all left

And obtained the following new goals

Proof step 87:
files[m0] = mkfile(m1, md0, m2, content), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), icache[ino] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), m ∈ icache, m0 ∈ files, ino ∈ files, m ∈ icache → icache[m].inode.ino = m ∧ (icache[m].dirty ⊃ icache[m].inode.ino ∈ files ∧ icache[m].inode.nlink = files[icache[m].inode.ino].nlink ∧ icache[m].inode.nsubdirs = 0 ∧ ¬ icache[m].inode.directory ; (m ∈ dirs ∨ m ∈ files) ∧ 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, files[icache[m].inode.ino].meta, false, files[icache[m].inode.ino].nlink, 0, files[icache[m].inode.ino].size) ) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache)[ino], ino = m, ino ∈ icache ∧ ¬ boolvar

Rule argument

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

Additional information

Used terms: m