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Proof step 110 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, asynced4 ↔ true, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, files = files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)], ino = m0, ino0 = m0, inode0 = mkinode(m0, md, false, # links(m0, dirs), 0, m), n = m, pcache = truncate(ino0, min(n, size), pcache0), size = m2, afs-cons(dirs, files0[m0, mkfile(m, md, # 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(pcache0, dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, m2 ≤ m, m2 % VFS_PAGE_SIZE + n0 ≤ # buf0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪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:= inode0.size).meta:= inode0.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode0.size).meta:= inode0.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode0.size).meta:= inode0.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[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache))), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 111:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, pcache = truncate(m0, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files0[m0, mkfile(m, md, # 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(pcache0, dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set# (mkinode (m0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( 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:= m) .meta:= md ;files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)][m0] ) .meta, false, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( 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:= m) .meta:= md ;files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)][m0] ) .nlink, 0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( 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:= m) .meta:= md ;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) .ino, m2 / VFS_PAGE_SIZE, some(fill(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if err ≠ ESUCCESS then buf-opt0 := none⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], dirs, files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]) ∧ dcache-cons (dcache, dirs, files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]) ∧ pcache-cons (pcache, dirs, files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, 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 (files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)