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: 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:
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


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