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Proof step 93 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, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 94:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), err = ESUCCESS, pcache = truncate(m3, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, 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) ]), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, m2 ≤ m, ¬ datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, 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[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], 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) ]) ∧ dcache-cons (dcache, 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) ]) ∧ pcache-cons (pcache, 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[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (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) ], icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)