### Nuprl Lemma : rel-restriction_wf

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[P:T ⟶ ℙ].  (R|P ∈ T ⟶ T ⟶ ℙ)`

Proof

Definitions occuring in Statement :  rel-restriction: `R|P` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel-restriction: `R|P` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ`
Lemmas referenced :  and_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].    (R|P  \mmember{}  T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{})

Date html generated: 2016_05_14-AM-06_06_02
Last ObjectModification: 2015_12_26-AM-11_32_39

Theory : relations

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