Nuprl Lemma : stable-union_wf
∀[X,T:Type]. ∀[P:T ⟶ X ⟶ ℙ]. (stable-union(X;T;i,x.P[i;x]) ∈ Type)
Proof
Definitions occuring in Statement :
stable-union: stable-union(X;T;i,x.P[i; x]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stable-union: stable-union(X;T;i,x.P[i; x]),
prop: ℙ,
exists: ∃x:A. B[x],
so_apply: x[s1;s2]
Lemmas referenced :
not_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
universeEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate
Latex:
\mforall{}[X,T:Type]. \mforall{}[P:T {}\mrightarrow{} X {}\mrightarrow{} \mBbbP{}]. (stable-union(X;T;i,x.P[i;x]) \mmember{} Type)
Date html generated:
2020_05_19-PM-09_36_15
Last ObjectModification:
2019_10_24-AM-09_55_58
Theory : int_1
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