Theorem: LO.System.Necessitation.nec! (Logic/Modal/Standard/HilbertStyle.lean)

State before:
F : Type u_1
inst✝⁵ : StandardModalLogicalConnective F
inst✝⁴ : DecidableEq F
S : Type u_2
inst✝³ : System F S
p q r : F
Γ Δ : List F
𝓢 : S
inst✝² : Classical 𝓢
inst✝¹ : System.NegationEquiv 𝓢
inst✝ : Necessitation 𝓢
⊢ 𝓢 ⊢! p → 𝓢 ⊢! □p
Tactic:
rintro ⟨hp⟩
State after:
case intro
F : Type u_1
inst✝⁵ : StandardModalLogicalConnective F
inst✝⁴ : DecidableEq F
S : Type u_2
inst✝³ : System F S
p q r : F
Γ Δ : List F
𝓢 : S
inst✝² : Classical 𝓢
inst✝¹ : System.NegationEquiv 𝓢
inst✝ : Necessitation 𝓢
hp : 𝓢 ⊢ p
⊢ 𝓢 ⊢! □p

State before:
case intro
F : Type u_1
inst✝⁵ : StandardModalLogicalConnective F
inst✝⁴ : DecidableEq F
S : Type u_2
inst✝³ : System F S
p q r : F
Γ Δ : List F
𝓢 : S
inst✝² : Classical 𝓢
inst✝¹ : System.NegationEquiv 𝓢
inst✝ : Necessitation 𝓢
hp : 𝓢 ⊢ p
⊢ 𝓢 ⊢! □p
Tactic:
exact ⟨nec hp⟩
State after:
no goals