Nuprl Lemma : isl_wf
∀[A,B:Type]. ∀[x:A + B]. (isl(x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
isl: isl(x),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
isl: isl(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
btrue_wf,
bfalse_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
lambdaFormation,
unionElimination,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A + B]. (isl(x) \mmember{} \mBbbB{})
Date html generated:
2019_06_20-AM-11_19_53
Last ObjectModification:
2018_08_21-PM-01_52_33
Theory : union
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