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Proof step 92 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, pcache = truncate(m0, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons (dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m0 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, ¬ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set# (mkinode (m0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .meta, false, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .nlink, 0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .size) .ino, m2 / VFS_PAGE_SIZE, some(fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ dcache-cons (dcache, dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ pcache-cons (pcache, dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files1 [m0, mkfile (m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 93:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, mkinode (m0, ( m0 ∈ files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .meta, false, ( m0 ∈ files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .nlink, 0, ( m0 ∈ files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .size) = mkinode(m3, md0, boolvar, m4, m5, m6), pcache = truncate(m0, m2, pcache0), afs-cons(dirs, files1), afs-cons (dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m0 ∈ files1, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set#(m3, m2 / VFS_PAGE_SIZE, some(fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false; err, pcache); if err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ dcache-cons (dcache, dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ pcache-cons (pcache, dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files1 [m0, mkfile (m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache))), m2 % VFS_PAGE_SIZE = 0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0

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] → [mkinode (m0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .meta, false, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .nlink, 0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .size), m3, md0, boolvar, m4, m5, 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: mkinode (m0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .meta, false, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .nlink, 0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .size), m3, md0, boolvar, m4, m5, m6