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Proof step 352 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), buf-opt.some?, afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache), ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data? ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = ino ∧ (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty ⊃ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino ∈ files0 ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.nlink = (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .nlink ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode = (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].meta, true, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].nlink, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].nsubdirs, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].size) ;mkinode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino, (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .meta, false, (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .nlink, 0, (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 353:
# buf-opt.buf = VFS_PAGE_SIZE, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode = mkinode(m, md, boolvar, m3, m4, m6), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data? ⊦ m = ino ∧ (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty ⊃ m ∈ files0 ∧ m3 = (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).nlink ∧ m4 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).meta, false, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).nlink, 0, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).size) ) ), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache [m0, mkientry (false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ] [ino ] .inode, m, md, boolvar, m3, m4, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache [m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ] [ino ] .inode, m, md, boolvar, m3, m4, m6