Nuprl Lemma : continuous-constant
∀[G:Type]. Continuous+(T.G)
Proof
Definitions occuring in Statement :
strong-type-continuous: Continuous+(T.F[T]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
nat: ℕ
Lemmas referenced :
nat_wf,
false_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
hypothesisEquality,
Error :universeIsType,
extract_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
Error :functionIsType,
Error :inhabitedIsType,
isectElimination,
universeEquality,
isectEquality,
equalitySymmetry,
equalityTransitivity,
rename,
lemma_by_obid,
lambdaFormation,
natural_numberEquality,
dependent_set_memberEquality,
lambdaEquality
Latex:
\mforall{}[G:Type]. Continuous+(T.G)
Date html generated:
2019_06_20-PM-00_27_46
Last ObjectModification:
2018_09_29-PM-09_27_25
Theory : subtype_1
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