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Proof step 112 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), err = ESUCCESS, 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) = mkinode(m3, md0, boolvar0, m4, m5, m6), pcache = truncate(m0, m2, pcache0), afs-cons(dirs, files0), 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)]), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set#(m3, 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))), m2 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), err = ESUCCESS, pcache = truncate(m3, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files0), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, 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(pcache0, dirs, files0), synced(dirs, icache, pcache0), m3 ∈ files0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set#(m3, 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[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]) ∧ dcache-cons (dcache, dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]) ∧ pcache-cons (pcache, dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, 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 (files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, 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)