[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 60 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, afs-cons(dirs, files0[m, mkfile(n, md, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m ∈ files0, m2 ≤ n, asynced1 → synced(files0, icache, pcache) ⊦ ⟪icache_set# (mkinode (m, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size), false ; err, icache); pcache_truncate# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ) .ino, m2, n ; err, pcache); inode := mkinode(m, md, false, # links(m, dirs), 0, n); ino := m; files := files0[m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]; pcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, m2 / VFS_PAGE_SIZE, some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); skip⟫ ( icache-cons(icache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 61:
# buf-opt.buf = VFS_PAGE_SIZE, (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ) = mkinode(m0, md0, boolvar, m3, m4, m5), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), err = ESUCCESS, buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(n, md, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m ∈ files0, m2 ≤ n, asynced1 → synced(files0, icache, pcache) ⊦ ⟪icache_set# (mkinode (m, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, files0 [m, files0 [m, files0 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size), false ; err, icache); pcache_truncate#(m0, m2, n; err, pcache); inode := mkinode(m, md, false, # links(m, dirs), 0, n); ino := m; files := files0[m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]; pcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, m2 / VFS_PAGE_SIZE, some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); skip⟫ ( icache-cons(icache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), 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] → [(m ∈ dirs ⊃ mkinode (m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files0 [m, files0 [m, files0 [m, mkfile (m1, md1, # links(m, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, files0 [m, files0 [m, files0 [m, mkfile (m1, md1, # links(m, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, files0 [m, files0 [m, files0 [m, mkfile (m1, md1, # links(m, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ), m0, md0, boolvar, m3, m4, m5]

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: (m ∈ dirs ⊃ mkinode (m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files0 [m, files0 [m, files0 [m, mkfile (m1, md1, # links(m, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, files0 [m, files0 [m, files0 [m, mkfile (m1, md1, # links(m, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, files0 [m, files0 [m, files0 [m, mkfile (m1, md1, # links(m, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ), m0, md0, boolvar, m3, m4, m5