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Proof step 2 from proof subdirs-del-entry (previous step)

ino ∈ dirs ⊦ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) -- str ;subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) )

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 3:
ino ∈ dirs, str ∈ entries ⊦ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) -- str ;subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) )

Rule argument

fma: str ∈ entries

Additional information

Used simplifier rules: ⊦ ¬ str ∈ entries → entries -- str = entries; (s) Used formulas: str ∈ entries