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Proof step 280 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), err = ESUCCESS, afs-cons(dirs, files0[m, mkfile(n, md, # links(m, dirs), content0 upto min(n, m2))]), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m ∈ files0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced2 → synced(files0, icache, pcache) ⊦ ⟪icache_set#(mkinode(m, md, false, # links(m, dirs), 0, n), false; err, icache); pcache_truncate# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2));files0[m]).meta, false, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2));files0[m]).nlink, 0, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2));files0[m]).size) ) .ino, m2, n ; err, pcache); inode := mkinode(m, md, false, # links(m, dirs), 0, n); ino := m; files := files0[m, mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2))]; asynced4 := false; if asynced4 then pcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, m2 / VFS_PAGE_SIZE, some(buf0).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 ≤ n ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 281:
# buf0 = VFS_PAGE_SIZE, (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2));files0[m]).meta, false, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2));files0[m]).nlink, 0, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2));files0[m]).size) ) = mkinode(m0, md0, boolvar0, m3, m4, m5), pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), err = ESUCCESS, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(n, md, # links(m, dirs), content0 upto min(n, m2))]), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, m ∈ files0, asynced2 → synced(files0, icache, pcache) ⊦ ⟪icache_set#(mkinode(m, md, false, # links(m, dirs), 0, n), false; err, icache); pcache_truncate#(m0, m2, n; err, pcache); inode := mkinode(m, md, false, # links(m, dirs), 0, n); ino := m; files := files0[m, mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2))]; asynced4 := false; if asynced4 then pcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, m2 / VFS_PAGE_SIZE, some(buf0).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 ≤ n ∧ 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 ∈ dirs ⊃ mkinode (m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m ∈ files0 ⊃ mkfile (n, md, # links(m, dirs), content0 upto min(n, m2)) ;files0[m] ) .meta, false, (m ∈ files0 ⊃ mkfile (n, md, # links(m, dirs), content0 upto min(n, m2)) ;files0[m] ) .nlink, 0, (m ∈ files0 ⊃ mkfile (n, md, # links(m, dirs), content0 upto min(n, m2)) ;files0[m] ) .size) ), m0, md0, boolvar0, m3, m4, m5]

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 ∈ dirs ⊃ mkinode (m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2)) ;files0[m] ) .meta, false, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2)) ;files0[m] ) .nlink, 0, (m ∈ files0 ⊃ mkfile(n, md, # links(m, dirs), content0 upto min(n, m2)) ;files0[m] ) .size) ), m0, md0, boolvar0, m3, m4, m5