Step
*
1
of Lemma
rel_star_symmetric
1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. ∀a,b:T. ((a R b)
⇒ (b R a))
4. a : T
5. b : T
6. a (R^*) b
⊢ b (R^*) a
BY
{ (Using [`R1',R^-1] (BackThruLemma `rel_star_monotonic`) THEN Auto) }
1
1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. ∀a,b:T. ((a R b)
⇒ (b R a))
4. a : T
5. b : T
6. a (R^*) b
⊢ R^-1 => R
2
1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. ∀a,b:T. ((a R b)
⇒ (b R a))
4. a : T
5. b : T
6. a (R^*) b
⊢ b (R^-1^*) a
Latex:
Latex:
1. [T] : Type
2. [R] : T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}
3. \mforall{}a,b:T. ((a R b) {}\mRightarrow{} (b R a))
4. a : T
5. b : T
6. a rel\_star(T; R) b
\mvdash{} b rel\_star(T; R) a
By
Latex:
(Using [`R1',R\^{}-1] (BackThruLemma `rel\_star\_monotonic`) THEN Auto)
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