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Proof step 203 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar2, mkinode(m7, md2, boolvar1, m8, m9, m10)), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar0, mkinode(m0, md0, boolvar, m4, m5, m6)), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), buf-opt.some?, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m3 ∈ files0, ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ino ∈ icache → m7 = ino ∧ (boolvar2 ⊃ ino ∈ files0 ∧ m8 = files0[ino].nlink ∧ m9 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md2, boolvar1, m8, m9, m10) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), ∀ key. key ∈ pcache0 → key.data?, ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files0 ∧ icache[ino0].inode.nlink = files0[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files0) ∧ 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, files0[icache[ino0].inode.ino].meta, false, files0[icache[ino0].inode.ino].nlink, 0, files0[icache[ino0].inode.ino].size) ) ) ⊦ m2 % VFS_PAGE_SIZE = 0, m0 = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m4 = (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m4, m5, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .meta, false, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink, 0, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: icache name: In-insert seq: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache subst: [ino, icache, ino0, ie] → [ino, icache, m3, mkientry (false, mkinode(m3, md, false, # links(m3, dirs), 0, m))] flags: <all paths>

Additional information

Used terms: ino, icache, m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))