Nuprl Lemma : stable__all
∀[T:Type]. ∀[P:T ⟶ ℙ]. ((∀x:T. Stable{P[x]}) ⇒ Stable{∀x:T. P[x]})
Proof
Definitions occuring in Statement :
stable: Stable{P},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T},
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
false: False,
not: ¬A,
member: t ∈ T,
uimplies: b supposing a,
stable: Stable{P},
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
stable_wf,
all_wf,
not_wf
Rules used in proof :
independent_functionElimination,
independent_isectElimination,
universeEquality,
functionEquality,
rename,
hypothesis,
functionExtensionality,
applyEquality,
cumulativity,
isectElimination,
extract_by_obid,
voidElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
introduction,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. Stable\{P[x]\}) {}\mRightarrow{} Stable\{\mforall{}x:T. P[x]\})
Date html generated:
2016_10_21-AM-09_34_56
Last ObjectModification:
2016_09_26-PM-00_47_01
Theory : core_2
Home
Index