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Proof step 3 from proof fsync-inode-overwrite (previous step)

inode.nlink = files0[inode.ino].nlink, inode.nsubdirs = 0, files = files0, icache0 = icache, icache-cons(icache, dirs, files0), inode.ino ∈ files0, ¬ inode.directory ⊦ [cache_fsync-inode#(; inode, err, dirs, files, icache, asynced)] (err = ESUCCESS → files[inode.ino] = (files0 ⊕ icache0)[inode.ino])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
¬ boolvar, files = files0, icache0 = icache, inode = mkinode(m, md, boolvar, m0, m1, m2), m0 = files0[m].nlink, m1 = 0, icache-cons(icache, dirs, files0), m ∈ files0 ⊦ [cache_fsync-inode#(; inode, err, dirs, files, icache, asynced)] (err = ESUCCESS → files[inode.ino] = (files0 ⊕ icache0)[inode.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