Nuprl Lemma : istype-inl-sqeq-inr
∀[a,b:Top]. istype(inl a ~ inr b )
Proof
Definitions occuring in Statement :
istype: istype(T),
uall: ∀[x:A]. B[x],
top: Top,
inr: inr x ,
inl: inl x,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
rev_implies: P ⇐ Q,
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
member_wf,
squash_wf,
true_wf,
istype-universe,
not-inl-sqeq-inr,
istype-sqequal,
equal_wf,
subtype_rel_self,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :universeIsType,
pointwiseFunctionality,
sqequalExtensionalEquality,
cut,
applyEquality,
thin,
instantiate,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
sqequalRule,
independent_functionElimination,
voidElimination,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
imageMemberEquality,
natural_numberEquality,
Error :inhabitedIsType
Latex:
\mforall{}[a,b:Top]. istype(inl a \msim{} inr b )
Date html generated:
2019_06_20-AM-11_19_58
Last ObjectModification:
2018_10_21-AM-09_30_48
Theory : union
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