### Nuprl Lemma : rel_equivalent_wf

`∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  (R1 `⇐⇒` R2 ∈ ℙ)`

Proof

Definitions occuring in Statement :  rel_equivalent: `R1 `⇐⇒` R2` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel_equivalent: `R1 `⇐⇒` R2` 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{}[R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (R1  \mLeftarrow{}{}\mRightarrow{}  R2  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-AM-06_04_35
Last ObjectModification: 2015_12_26-AM-11_33_11

Theory : relations

Home Index