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Proof step 301 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, truncate(m0, min(m5, m2), pcache)[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(boolvar0, inode), buf-opt.some?, afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache), ino ∈ dirs, m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache → key.data?, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, ( ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 302:
# buf-opt.buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar0, inode), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), truncate(m0, min(m5, m2), pcache)[datakey(ino, n)] = mkpentry(boolvar, buf), icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, inode0), buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache), m0 ∈ files0, ino ∈ dirs, ino ∈ icache → ¬ boolvar0, asynced1 → synced(files0, icache, pcache), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, ∀ key. key ∈ pcache → key.data? ⊦ (ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache [m0, mkientry (false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ] [ino ], boolvar1, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache [m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5)) ] [ino ], boolvar1, inode0