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Proof step 55 from proof refine-truncate-buff-some (previous step)

# 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
# buf-opt0.buf = VFS_PAGE_SIZE, (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) ) = mkinode(m3, md1, boolvar, m4, m5, m6), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, buf-opt0.some?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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#(m3, 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), 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] → [(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) ), m3, md1, 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: (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) ), m3, md1, boolvar, m4, m5, m6