Nuprl Lemma : sq_stable__uni_sat
∀[T:Type]. ∀a:T. ∀[Q:T ⟶ ℙ]. ((∀x:T. SqStable(Q[x])) ⇒ SqStable(a = !x:T. Q[x]))
Proof
Definitions occuring in Statement :
uni_sat: a = !x:T. Q[x],
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 :
uni_sat: a = !x:T. Q[x],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P)
Lemmas referenced :
sq_stable__and,
all_wf,
equal_wf,
sq_stable__all,
sq_stable__equal,
squash_wf,
sq_stable_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
isect_memberEquality,
lambdaEquality,
functionEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
universeEquality,
because_Cache,
axiomEquality,
Error :functionIsType,
Error :inhabitedIsType,
Error :universeIsType
Latex:
\mforall{}[T:Type]. \mforall{}a:T. \mforall{}[Q:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. SqStable(Q[x])) {}\mRightarrow{} SqStable(a = !x:T. Q[x]))
Date html generated:
2019_06_20-AM-11_18_16
Last ObjectModification:
2018_09_26-AM-10_25_18
Theory : core_2
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