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Proof step 83 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, afs-cons (dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache, dirs, files1), synced(dirs, icache, pcache), m0 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, ¬ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced2 → synced(files1, icache, pcache) ⊦ ⟪pcache_truncate#(m0, m2, m; err, pcache); inode0 := mkinode(m0, md, false, # links(m0, dirs), 0, m); ino := m0; files := files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], 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:= 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(files1[m0].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := 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)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 84:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, ino = m0, n = m, size = m2, afs-cons(dirs, files1), afs-cons (dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache, dirs, files1), synced(dirs, icache, pcache), m2 / VFS_PAGE_SIZE ∈ content0, m0 ∈ files1, m2 ≤ m, asynced2 → synced(files1, icache, pcache) ⊦ ⟪if ∀ key. key ∈ pcache → key.data? then pcache := truncate(ino, min(n, size), pcache) else abort; inode0 := mkinode(m0, md, false, # links(m0, dirs), 0, m); ino := m0; files := files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], 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:= 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(files1[m0].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := 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, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: pcache_truncate#(INO, SIZE, N; ERR, PCACHE) {if ∀ key. key ∈ PCACHE → key.data? then PCACHE := truncate(INO, min(N, SIZE), PCACHE) else abort };