Nuprl Lemma : uni_sat_wf
∀[T:Type]. ∀[a:T]. ∀[Q:T ⟶ ℙ]. (a = !x:T. Q[x] ∈ ℙ)
Proof
Definitions occuring in Statement :
uni_sat: a = !x:T. Q[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uni_sat: a = !x:T. Q[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
applyEquality,
hypothesisEquality,
hypothesis,
thin,
lambdaEquality,
sqequalHypSubstitution,
universeEquality,
extract_by_obid,
isectElimination,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :inhabitedIsType,
Error :universeIsType,
isect_memberEquality,
cumulativity,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[Q:T {}\mrightarrow{} \mBbbP{}]. (a = !x:T. Q[x] \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_18_10
Last ObjectModification:
2018_09_26-AM-10_25_16
Theory : core_2
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