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: function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  rel-restriction: R|P rel_implies: R1 => R2 infix_ap: y uall: [x:A]. B[x] all: x:A. B[x] implies:  Q and: P ∧ Q member: t ∈ T prop:
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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