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Proof step 1 from proof subdirs-del-mod-size (conclusion)

⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n0, n1, entries) → subdirs(p_ino, dirs[p_ino, mkdir(m0, md, n0, n2, entries -- str)]) = (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(p_ino, dirs) -- str;subdirs(p_ino, dirs))

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(m0, md, n0, n2, entries -- str)]) = (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(p_ino, dirs) -- str;subdirs(p_ino, dirs))

Proof step 1 from proof subdirs-del-mod-size (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information