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Proof step 215 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar0, mkinode(m0, md0, boolvar, m4, m5, m6)), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), synced(dirs, icache, pcache0), ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m3 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files1 ∧ icache[ino].inode.nlink = files1[icache[ino].inode.ino].nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files1) ∧ 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, files1[icache[ino].inode.ino].meta, false, files1[icache[ino].inode.ino].nlink, 0, files1[icache[ino].inode.ino].size) ) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files1 ∧ icache[ino0].inode.nlink = files1[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files1) ∧ 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, files1[icache[ino0].inode.ino].meta, false, files1[icache[ino0].inode.ino].nlink, 0, files1[icache[ino0].inode.ino].size) ) ), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 = ino ∧ (boolvar0 ⊃ ino ∈ files1 ∧ m4 = (ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files1) ∧ 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(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .meta, false, (ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .nlink, 0, (ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 216:
icache[ino].inode = mkinode(m7, md2, boolvar1, m8, m9, m10), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar0, mkinode(m0, md0, boolvar, m4, m5, m6)), files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons(dirs, files1), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m2 ≤ m, ino ∈ icache → m7 = ino ∧ (icache[ino].dirty ⊃ m7 ∈ files1 ∧ m8 = files1[m7].nlink ∧ m9 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files1) ∧ icache[ino].inode = (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files1[m7].meta, false, files1[m7].nlink, 0, files1[m7].size) ) ), asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files1 ∧ icache[ino0].inode.nlink = files1[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files1) ∧ 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, files1[icache[ino0].inode.ino].meta, false, files1[icache[ino0].inode.ino].nlink, 0, files1[icache[ino0].inode.ino].size) ) ) ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 = ino ∧ (boolvar0 ⊃ ino ∈ files1 ∧ m4 = (ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files1) ∧ 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(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .meta, false, (ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .nlink, 0, (ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[ino] ) .size) ) )

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[ino].inode, m7, md2, boolvar1, m8, m9, m10]

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[ino].inode, m7, md2, boolvar1, m8, m9, m10