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Proof step 74 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, pcache = truncate(m0, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, afs-cons (dirs, files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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), m0 ∈ files0, m2 ≤ m, asynced1 → 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)][m0] ) .size) .ino, m2 / VFS_PAGE_SIZE, some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); skip⟫ ( 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(buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced1 → synced (files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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 75:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, mkinode (m0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] ⊃ ( files0 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)][m0] ) .size) = mkinode(m3, md0, boolvar, m4, m5, m6), pcache = truncate(m0, m2, pcache0), buf-opt.some?, afs-cons(dirs, files0), afs-cons (dirs, files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set#(m3, m2 / VFS_PAGE_SIZE, some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false; err, pcache); skip⟫ ( 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(buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced1 → synced (files0[m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, 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

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 ∈ files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, 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(buf-opt.buf, 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 ∈ files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, 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(buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] ⊃ ( files0 [m0, mkfile (m1, md1, # links(m0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (buf-opt.buf, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ] [m0 ] ) .size), m3, md0, boolvar, m4, m5, m6