### Nuprl Lemma : rel_star_trans

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  ∀x,y,z:T.  ((x R y) `` (y (R^*) z) `` (x (R^*) z))`

Proof

Definitions occuring in Statement :  rel_star: `R^*` uall: `∀[x:A]. B[x]` prop: `ℙ` infix_ap: `x f y` all: `∀x:A. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` infix_ap: `x f y`
Lemmas referenced :  rel_star_transitivity rel_rel_star rel_star_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality independent_functionElimination dependent_functionElimination hypothesis applyEquality Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  universeEquality

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

Date html generated: 2019_06_20-PM-00_30_52
Last ObjectModification: 2018_09_26-PM-00_43_06

Theory : relations

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