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Proof step 1 from proof subdirs-put (conclusion)

⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n0, n1, entries) → subdirs(p_ino, dirs[p_ino, mkdir(m, md, n0, n1, entries[str, ino])]) = (subdirs(p_ino, dirs) \ (str ∈ entries ∧ entries[str] ∈ dirs ⊃ {str} ;∅)) ∪ (ino ∈ dirs ⊃ {str} ;∅)

System applied rule normalize

And obtained the following new goals

Proof step 2:
dirs[p_ino] = mkdir(m, md, n0, n1, entries), p_ino ∈ dirs ⊦ subdirs(p_ino, dirs[p_ino, mkdir(m, md, n0, n1, entries[str, ino])]) = (subdirs(p_ino, dirs) \ (str ∈ entries ∧ entries[str] ∈ dirs ⊃ {str} ;∅)) ∪ (ino ∈ dirs ⊃ {str} ;∅)

Proof step 1 from proof subdirs-put (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information