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Proof step 54 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, asynced ↔ false, asynced4 ↔ true, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt1 = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)), dirs = cache_dirs, err = ESUCCESS, files = cache_files[m, mkfile(m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)], ino = inode.ino, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, n), inode1 = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ), buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ files, m ∈ cache_files, m2 % VFS_PAGE_SIZE + n0 ≤ # buf-opt0.buf, m2 ≤ n, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_set#(inode1, asynced; err, cache_icache); pcache_truncate#(inode1.ino, m2, n; err, cache_pcache); if asynced4 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt1.buf, asynced; err, cache_pcache); if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt1 := none⟫ ⟨inode0 := mkinode(m, md, false, # links(m, cache_dirs), 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta] ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced0) ∧ buf-opt1 = buf-opt0 ∧ inode1 = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m2 ≤ n, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_set# (mkinode (m, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size), false ; err, cache_icache); pcache_truncate# ((m ∈ cache_dirs ⊃ mkinode(m, cache_dirs[m].meta, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size) ;mkinode (m, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ) .ino, m2, n ; err, cache_pcache); inode1 := (m ∈ cache_dirs ⊃ mkinode(m, cache_dirs[m].meta, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size) ;mkinode (m, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .meta, false, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .nlink, 0, cache_files [m, cache_files [m, cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m ] .size:= n ] [m ] .meta:= md ] [m ] .size) ); buf-opt1 := some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)); asynced4 := true; if asynced4 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt1.buf, false; err, cache_pcache); if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt1 := none⟫ ⟨inode0 := mkinode(m, md, false, # links(m, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs, buf-opt := buf-opt0; cache_dirs3 := cache_dirs; afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m, mkfile(n, md, # links(m, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced0) ∧ buf-opt1 = buf-opt0 ∧ inode1 = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)