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Proof step 3 from proof fsync-others-unchanged (previous step)

inode.nlink = files0[inode.ino].nlink, inode.nsubdirs = 0, files = files0, icache = icache0, pcache = pcache0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache0), inode.ino ∈ files0, ¬ inode.directory ⊦ [cache_fsync#(inode, bv, bv0; dirs, files, icache, pcache, asynced; err)] ∀ ino. ino ≠ inode.ino ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
¬ boolvar, files = files0, icache = icache0, inode = mkinode(m, md, boolvar, m0, m1, m2), m0 = files0[m].nlink, m1 = 0, pcache = pcache0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache0), m ∈ files0 ⊦ [cache_fsync#(inode, bv, bv0; dirs, files, icache, pcache, asynced; err)] ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

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] → [inode, m, md, boolvar, m0, m1, m2]

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: inode, m, md, boolvar, m0, m1, m2