### Nuprl Lemma : binrel_eqv_wf

`∀[T:Type]. ∀[E,E':T ⟶ T ⟶ ℙ].  (E <≡>{T} E' ∈ ℙ)`

Proof

Definitions occuring in Statement :  binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` prop: `ℙ`
Lemmas referenced :  all_wf iff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[E,E':T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (E  <\mequiv{}>\{T\}  E'  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-PM-03_54_37
Last ObjectModification: 2015_12_26-PM-06_56_08

Theory : relations2

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