### Nuprl Lemma : rel_inverse_star

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  ∀x,y:T.  (x R^*^-1 ⇐⇒ (R^-1^*) y)

Proof

Definitions occuring in Statement :  rel_inverse: R^-1 rel_star: R^* uall: [x:A]. B[x] prop: infix_ap: y all: x:A. B[x] iff: ⇐⇒ Q function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] all: x:A. B[x] iff: ⇐⇒ Q and: P ∧ Q implies:  Q member: t ∈ T prop: infix_ap: y rev_implies:  Q rel_star: R^* rel_inverse: R^-1 exists: x:A. B[x]
Lemmas referenced :  rel_inverse_wf rel_star_wf rel_exp_wf rel_inverse_exp
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  lambdaFormation independent_pairFormation applyEquality cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  universeEquality sqequalRule productElimination dependent_pairFormation dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    \mforall{}x,y:T.    (x  rel\_star(T;  R)\^{}-1  y  \mLeftarrow{}{}\mRightarrow{}  x  rel\_star(T;  R\^{}-1)  y)

Date html generated: 2019_06_20-PM-00_30_55
Last ObjectModification: 2018_09_26-PM-00_41_50

Theory : relations

Home Index