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Proof step 79 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), files1 [m0, files1 [m0, 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) ] [m0 ] .size:= m5 ] [m0 ] .meta:= md0 ] [m0 ] = mkfile(m, md, m3, content), err = ESUCCESS, afs-cons(dirs, files1), afs-cons (dirs, files1 [m0, mkfile(m5, md0, # 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 ≤ m5, asynced2 → synced(files1, icache, pcache) ⊦ ⟪icache_set#(mkinode(m0, md, false, m3, 0, m), false; err, icache); pcache_truncate#(m0, m2, m5; err, pcache); inode := mkinode(m0, md0, false, # links(m0, dirs), 0, m5); 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:= inode.size).meta:= inode.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.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, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), m2 % VFS_PAGE_SIZE = 0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
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), 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, ¬ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced2 → synced(files1, icache, pcache) ⊦ ⟪icache_set#(mkinode(m0, md, false, # links(m0, dirs), 0, m), false; err, icache); pcache_truncate#(m0, m2, m; err, pcache); inode := 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:= inode.size).meta:= inode.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.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, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ 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)