### Nuprl Lemma : rel-restriction-implies

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[P:T ⟶ ℙ].  R|P => R`

Proof

Definitions occuring in Statement :  rel-restriction: `R|P` rel_implies: `R1 => R2` uall: `∀[x:A]. B[x]` prop: `ℙ` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel-restriction: `R|P` rel_implies: `R1 => R2` infix_ap: `x f y` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` and: `P ∧ Q` member: `t ∈ T` prop: `ℙ`
Lemmas referenced :  and_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin hypothesis cut lemma_by_obid isectElimination applyEquality hypothesisEquality functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].    R|P  =>  R

Date html generated: 2016_05_14-AM-06_06_03
Last ObjectModification: 2015_12_26-AM-11_32_20

Theory : relations

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