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Proof step 72 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, ino = m0, n = m, pcache = truncate(ino, min(n, size), pcache0), size = m2, 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? ⊦ ⟪files := 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)]; pcache_set# ((m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = m0 ∧ m0 ∈ files ⊃ (files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size).meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ;files[m0] ) .meta, false, (m0 = m0 ∧ m0 ∈ files ⊃ (files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size).meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ;files[m0] ) .nlink, 0, (m0 = m0 ∧ m0 ∈ files ⊃ (files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size).meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ;files[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, files [m0, (m0 ∈ files ⊃ files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size;files[m0]) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ]) ∧ dcache-cons (dcache, dirs, files [m0, (m0 ∈ files ⊃ files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size;files[m0]) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ]) ∧ pcache-cons (pcache, dirs, files [m0, (m0 ∈ files ⊃ files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size;files[m0]) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced1 → synced (files [m0, (m0 ∈ files ⊃ files[m0].size:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size;files[m0]) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache))), m2 % VFS_PAGE_SIZE = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 73:
# 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, ino = m0, n = m, pcache = truncate(ino, min(n, size), pcache0), size = m2, 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 % VFS_PAGE_SIZE + n0 ≤ # buf-opt.buf, m2 ≤ m, asynced1 → 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 = 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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ;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 = 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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ;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 = 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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size) .meta:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ;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(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] [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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size ;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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ]) ∧ dcache-cons (dcache, dirs, 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, ( 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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size ;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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ]) ∧ pcache-cons (pcache, dirs, 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, ( 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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size ;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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced1 → synced (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, ( 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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).size ;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:= mkinode(m0, md, false, # links(m0, dirs), 0, m).meta ], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache))), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)