### Nuprl Lemma : rel_finite_wf

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

Proof

Definitions occuring in Statement :  rel_finite: `rel_finite(T;R)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rel_finite: `rel_finite(T;R)` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` infix_ap: `x f y` so_apply: `x[s]`
Lemmas referenced :  all_wf exists_wf list_wf l_member_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality hypothesis functionEquality applyEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (rel\_finite(T;R)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-PM-03_51_46
Last ObjectModification: 2015_12_26-PM-06_57_28

Theory : relations2

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