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Proof step 29 from proof map-del (conclusion)

⊦ (r => o * P)(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = o

User applied rule case distinction

And obtained the following new goals

Proof step 8:
(r => o * P)(H) ⊦ P(H -- r) ∧ r ∈ H ∧ H[r] = o

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]