Nuprl Lemma : invert-union_wf
∀[A,B:Type]. ∀[x:A + B]. (invert-union(x) ∈ B + A)
Proof
Definitions occuring in Statement :
invert-union: invert-union(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
invert-union: invert-union(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
lambdaFormation,
unionElimination,
inrEquality,
inlEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A + B]. (invert-union(x) \mmember{} B + A)
Date html generated:
2019_10_15-AM-11_07_01
Last ObjectModification:
2018_08_21-PM-01_58_51
Theory : general
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