[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 78 from proof eq-io-evict (previous step)

⟨if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else if files[ino].nlink = 0 then files := files -- ino⟩ (ESUCCESS = err0 ∧ dirs = dirs0 ∧ files = files0), asynced ↔ asynced0, files1[m] = mkfile(m0, md0, m1, content), dirs = dirs1, files = files1, ino = inode.ino, inode = mkinode(m, md, false, m1, 0, m2), pre-evict(inode, dirs, files), m ∈ files1 ⊦ m = ROOT_INO, m1 = 0, m ∈ dirs1, ESUCCESS = err0 ∧ dirs1 = dirs0 ∧ files1 = files0

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 79:
⟨if dirs[ino].nlink = 0 then dirs := dirs -- ino⟩ (ESUCCESS = err0 ∧ dirs = dirs0 ∧ files = files0), asynced ↔ asynced0, files1[m] = mkfile(m0, md0, m1, content), dirs = dirs1, files = files1, ino = inode.ino, inode = mkinode(m, md, false, m1, 0, m2), pre-evict(inode, dirs, files), m ∈ files1, ino ∈ dirs ⊦ m = ROOT_INO, m1 = 0, m ∈ dirs1, ESUCCESS = err0 ∧ dirs1 = dirs0 ∧ files1 = files0
Proof step 82:
⟨if files[ino].nlink = 0 then files := files -- ino⟩ (ESUCCESS = err0 ∧ dirs = dirs0 ∧ files = files0), asynced ↔ asynced0, files1[m] = mkfile(m0, md0, m1, content), dirs = dirs1, files = files1, ino = inode.ino, inode = mkinode(m, md, false, m1, 0, m2), pre-evict(inode, dirs, files), m ∈ files1 ⊦ m = ROOT_INO, m1 = 0, m ∈ dirs1, ino ∈ dirs, ESUCCESS = err0 ∧ dirs1 = dirs0 ∧ files1 = files0

Proof step 78 from proof eq-io-evict (previous step)

Heuristic conditional left split applied rule if left

And obtained the following new goals

Rule argument

Additional information