Nuprl Lemma : nary-rel-predicate_wf
∀[T:Type]. ∀[n:ℕ]. ∀[R:n-aryRel(T)]. ([[R]] ∈ n:ℕ ⟶ (ℕn ⟶ T) ⟶ ℙ)
Proof
Definitions occuring in Statement :
nary-rel-predicate: [[R]],
nary-rel: n-aryRel(T),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nary-rel-predicate: [[R]],
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
nary-rel: n-aryRel(T),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
le_wf,
subtype_rel_dep_function,
int_seg_wf,
int_seg_subtype,
false_wf,
nat_wf,
nary-rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
natural_numberEquality,
independent_isectElimination,
because_Cache,
independent_pairFormation,
lambdaFormation,
universeEquality,
functionEquality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[R:n-aryRel(T)]. ([[R]] \mmember{} n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_07_19
Last ObjectModification:
2015_12_26-PM-07_55_07
Theory : fan-theorem
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