Nuprl Lemma : union-eta
∀d:Top + Top. ((d ~ inl outl(d)) ∨ (d ~ inr outr(d) ))
Proof
Definitions occuring in Statement :
outr: outr(x),
outl: outl(x),
top: Top,
all: ∀x:A. B[x],
or: P ∨ Q,
inr: inr x ,
inl: inl x,
union: left + right,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
outl: outl(x),
outr: outr(x),
member: t ∈ T,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
top: Top
Lemmas referenced :
top_wf,
istype-inl-sqeq-inr,
istype-void,
istype-inr-sqeq-inl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
unionElimination,
thin,
sqequalRule,
Error :unionIsType,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
because_Cache,
Error :inlFormation_alt,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :inrFormation_alt
Latex:
\mforall{}d:Top + Top. ((d \msim{} inl outl(d)) \mvee{} (d \msim{} inr outr(d) ))
Date html generated:
2019_06_20-AM-11_20_01
Last ObjectModification:
2018_10_15-PM-11_28_17
Theory : union
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