### Nuprl Lemma : rel_exp_wf

`∀[n:ℕ]. ∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (R^n ∈ T ⟶ T ⟶ ℙ)`

Proof

Definitions occuring in Statement :  rel_exp: `R^n` nat: `ℕ` 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` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` rel_exp: `R^n` eq_int: `(i =z j)` subtract: `n - m` ifthenelse: `if b then t else f fi ` btrue: `tt` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` uiff: `uiff(P;Q)` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` bool: `𝔹` unit: `Unit` it: `⋅` bfalse: `ff` exists: `∃x:A. B[x]` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  unionElimination independent_pairFormation productElimination addEquality applyEquality voidEquality intEquality minusEquality because_Cache equalityElimination dependent_pairFormation promote_hyp instantiate productEquality functionExtensionality

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

Date html generated: 2019_06_20-PM-00_30_19
Last ObjectModification: 2018_09_26-PM-00_39_26

Theory : relations

Home Index