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Proof step 46 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, ino ∈ icache ⊦ m0 = m ∧ (∀ ino0. ino0 ≠ m ∧ ino0 ∈ files0 → (files0 ⊕ icache[ino, icache[ino].dirty:= asynced])[ino0] = (files0 ⊕ icache0)[ino0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
icache0[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), icache-cons(icache0, dirs, files0), m ∈ icache0, m0 ∈ dirs ⊦ m0 = m

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite-other: ⊦ ino ≠ m → (files ⊕ icache[m, ie])[ino] = (files ⊕ icache)[ino];