### Nuprl Lemma : rel-connected_transitivity

`∀[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-connected: `x──R⟶y` uall: `∀[x:A]. B[x]` prop: `ℙ` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel-connected: `x──R⟶y` uall: `∀[x:A]. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` infix_ap: `x f y`
Lemmas referenced :  rel_star_transitivity rel_star_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality independent_functionElimination hypothesis applyEquality functionEquality cumulativity universeEquality

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

Date html generated: 2016_05_13-PM-04_19_18
Last ObjectModification: 2015_12_26-AM-11_33_39

Theory : relations

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