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Proof step 298 from proof inv-truncate-buff-none-uncached (previous step)

files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(files0, icache, pcache0), ino ∈ files0, m0 ∈ files0, ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, ( 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) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 299:
truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(boolvar0, inode), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(files0, icache, pcache0), m0 ∈ files0, ino ∈ files0, ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, ( 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) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino], boolvar0, inode