### Nuprl Lemma : binrel_eqv_transitivity

`∀[T:Type]. ∀[Q,R,S:T ⟶ T ⟶ ℙ].  ((Q <≡>{T} R) `` (R <≡>{T} S) `` (Q <≡>{T} S))`

Proof

Definitions occuring in Statement :  binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` prop: `ℙ` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` member: `t ∈ T` prop: `ℙ` rev_implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  all_wf iff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation independent_pairFormation cut hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality productElimination independent_functionElimination because_Cache applyEquality lemma_by_obid isectElimination lambdaEquality functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[Q,R,S:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    ((Q  <\mequiv{}>\{T\}  R)  {}\mRightarrow{}  (R  <\mequiv{}>\{T\}  S)  {}\mRightarrow{}  (Q  <\mequiv{}>\{T\}  S))

Date html generated: 2016_05_14-PM-03_54_40
Last ObjectModification: 2015_12_26-PM-06_56_07

Theory : relations2

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