Nuprl Lemma : rel-connected_transitivity

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


Proof




Definitions occuring in Statement :  rel-connected: x──R⟶y uall: [x:A]. B[x] prop: implies:  Q function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  rel-connected: x──R⟶y uall: [x:A]. B[x] implies:  Q member: t ∈ T prop: infix_ap: 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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