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Proof step 36 from proof subdirs-put (previous step)

dirs[p_ino] = mkdir(m, md, n0, n1, entries), str0 ∈ entries, entries[str0] ∈ dirs, p_ino ∈ dirs, ¬ str ∈ entries ∨ ¬ entries[str] ∈ dirs ⊦ # subdirs(p_ino, dirs) = 0, str0 = str, subdirs(p_ino, dirs) = ∅, ino ∈ dirs, str0 ∈ (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(p_ino, dirs) -- str;subdirs(p_ino, dirs)), str0 ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
dirs[p_ino] = mkdir(m, md, n0, n1, entries), p_ino ∈ dirs, entries[str0] ∈ dirs, str0 ∈ entries, ¬ str ∈ entries ∨ ¬ entries[str] ∈ dirs ⊦ # subdirs(p_ino, dirs) = 0, str0 = str, subdirs(p_ino, dirs) = ∅, str0 ∈ (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(p_ino, dirs) -- str;subdirs(p_ino, dirs)), ino ∈ dirs

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ ∅; (s)