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Proof step 44 from proof fsync-inode-others-unchanged (previous step)

asynced ↔ false, dirs[m0] = mkdir(m1, md0, m2, m3, entries), icache0[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), err = ESUCCESS, icache = icache1, icache1 = icache0, ino = m, icache-cons(icache0, dirs, files0), m0 ∈ dirs, m ∈ icache0 ⊦ [if ino ∈ icache then icache[ino].dirty := asynced else err := EFAIL] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache)[ino] = (files0 ⊕ icache0)[ino]))

Heuristic conditional right split applied rule if right

And obtained the following new goals

Proof step 45:
asynced ↔ false, icache0[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), err = ESUCCESS, icache = icache1, icache1 = icache0, ino = m, icache-cons(icache0, dirs, files0), ino ∈ icache, m ∈ icache0, m0 ∈ dirs ⊦ [icache[ino].dirty := asynced] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache)[ino] = (files0 ⊕ icache0)[ino]))
Proof step 51:
asynced ↔ false, icache0[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), err = ESUCCESS, icache = icache1, icache1 = icache0, ino = m, icache-cons(icache0, dirs, files0), m ∈ icache0, m0 ∈ dirs ⊦ [err := EFAIL] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache)[ino] = (files0 ⊕ icache0)[ino])), ino ∈ icache

Proof step 44 from proof fsync-inode-others-unchanged (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

Additional information