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Proof step 97 from proof fsync-inode-others-unchanged (previous step)

err = ESUCCESS, icache = icache0, icache-cons(icache0, dirs, files0), inode0.ino ∈ icache0, ¬ icache0[inode0.ino].dirty ⊦ [icache_set_status#(inode0.ino, false; err, icache)] ∀ ino. ino ≠ inode0.ino ∧ ino ∈ files0 → (files0 ⊕ icache)[ino] = (files0 ⊕ icache0)[ino]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 98:
err = ESUCCESS, icache = icache0, inode0 = mkinode(m, md, boolvar, m0, m1, m2), icache-cons(icache0, dirs, files0), m ∈ icache0 ⊦ [icache_set_status#(m, false; err, icache)] ∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache)[ino] = (files0 ⊕ icache0)[ino], icache0[m].dirty

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] → [inode0, 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: inode0, m, md, boolvar, m0, m1, m2