Nuprl Lemma : flip-union_wf
∀[X:Type]. ∀[x:X + X]. (flip-union(x) ∈ X + X)
Proof
Definitions occuring in Statement :
flip-union: flip-union(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
flip-union: flip-union(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
because_Cache,
lambdaFormation,
unionElimination,
inrEquality,
inlEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
unionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[x:X + X]. (flip-union(x) \mmember{} X + X)
Date html generated:
2020_05_20-AM-08_59_07
Last ObjectModification:
2018_08_21-PM-02_01_46
Theory : lattices
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