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Proof step 446 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, ∀ ino. ino ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] → icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty ⊃ valid-file-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ) ⊦ synced(dirs, icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))], pcache)

User applied rule all left

And obtained the following new goals

Proof step 447:
icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache, m0 ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] → icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].inode.ino = m0 ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].dirty ⊃ valid-file-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].inode, dirs, files) ;valid-ino(m0, dirs, files) ∧ valid-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][m0].inode, dirs, files) ), ∀ ino. ino ∈ icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))] → icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode.ino = ino ∧ (icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty ⊃ valid-file-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].inode, dirs, files) ) ⊦ synced(dirs, icache[m0, mkientry(true, mkinode(m0, md, boolvar0, m1, m3, m2))], pcache)

Rule argument

pos: left 9 terms: m0 abort: F discard: F computed: T

Additional information

Used terms: m0