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Proof step 96 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = 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(buf0, 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(buf0, 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(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ) = mkinode(m0, md0, boolvar0, m3, m4, m5), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), err = ESUCCESS, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(n, md, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, 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, datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, m2 ≤ n, asynced2 → 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(buf0, 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(buf0, 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(buf0, 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(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]; asynced4 := true; if asynced4 then 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(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt0 := none⟫ ( 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) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), m2 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, 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), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache, m0 ∈ files0, m2 ≤ m5, asynced2 → synced(files0, icache, pcache) ⊦ ⟪icache_set# (mkinode (m0, files0 [m0, files0 [m0, files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m5 ] [m0 ] .meta:= md0 ] [m0 ] .meta, false, files0 [m0, files0 [m0, files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m5 ] [m0 ] .meta:= md0 ] [m0 ] .nlink, 0, files0 [m0, files0 [m0, files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m5 ] [m0 ] .meta:= md0 ] [m0 ] .size), false ; err, icache); pcache_truncate#(m0, m2, m5; err, pcache); inode := mkinode(m0, md0, false, # links(m0, dirs), 0, m5); ino := m0; files := files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]; asynced4 := true; if asynced4 then pcache_set# ((m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).size) ) .ino, m2 / VFS_PAGE_SIZE, some(fill(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt0 := none⟫ ( 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) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, 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)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ 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)