### Nuprl Lemma : R-closed_wf

`∀[T:Type]. ∀[X:T ⟶ ℙ]. ∀[R:T ⟶ T ⟶ ℙ].  (R-closed(T;x.X[x];a,b.R[a;b]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  R-closed: `R-closed(T;x.X[x];a,b.R[a; b])` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` R-closed: `R-closed(T;x.X[x];a,b.R[a; b])` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s1;s2]` so_apply: `x[s]`
Lemmas referenced :  all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[X:T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (R-closed(T;x.X[x];a,b.R[a;b])  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-PM-04_08_51
Last ObjectModification: 2015_12_26-PM-07_54_54

Theory : fan-theorem

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