Step
*
of Lemma
rel_plus_iff
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x,z:T. (x R+ z
⇐⇒ ∃y:T. ((x (R^*) y) ∧ (y R z)))
BY
{ (Auto THEN ExRepD) }
1
1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. x : T@i
4. z : T@i
5. x R+ z@i
⊢ ∃y:T. ((x (R^*) y) ∧ (y R z))
2
1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. x : T@i
4. z : T@i
5. y : T@i
6. x (R^*) y@i
7. y R z@i
⊢ x R+ z
Latex:
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x,z:T. (x R\msupplus{} z \mLeftarrow{}{}\mRightarrow{} \mexists{}y:T. ((x rel\_star(T; R) y) \mwedge{} (y R z)))
By
Latex:
(Auto THEN ExRepD)
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