### Nuprl Lemma : rel_plus_wf

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

Proof

Definitions occuring in Statement :  rel_plus: `R+` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel_plus: `R+` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` infix_ap: `x f y` subtype_rel: `A ⊆r B` prop: `ℙ` so_apply: `x[s]` exists: `∃x:A. B[x]`
Lemmas referenced :  exists_wf nat_plus_wf rel_exp_wf nat_plus_subtype_nat
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis applyEquality hypothesisEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality isect_memberEquality because_Cache

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

Date html generated: 2016_05_14-PM-03_51_27
Last ObjectModification: 2015_12_26-PM-06_57_30

Theory : relations2

Home Index