Nuprl Lemma : sq_stable__all
∀[A:Type]. ∀[P:A ⟶ ℙ]. ((∀x:A. SqStable(P[x])) ⇒ SqStable(∀x:A. P[x]))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(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 :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T
Lemmas referenced :
squash_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
Error :functionIsType,
Error :universeIsType,
universeEquality,
dependent_functionElimination,
independent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:A. SqStable(P[x])) {}\mRightarrow{} SqStable(\mforall{}x:A. P[x]))
Date html generated:
2019_06_20-AM-11_15_23
Last ObjectModification:
2018_09_26-AM-09_59_31
Theory : core_2
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