Nuprl Lemma : respects-equality-trivial
∀[T:Type]. respects-equality(T;T)
Proof
Definitions occuring in Statement :
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
istype-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
hypothesis,
sqequalRule,
Error :equalityIsType4,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
because_Cache,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
Error :lambdaEquality_alt,
dependent_functionElimination,
thin,
axiomEquality,
Error :functionIsTypeImplies,
universeEquality
Latex:
\mforall{}[T:Type]. respects-equality(T;T)
Date html generated:
2019_06_20-AM-11_13_41
Last ObjectModification:
2018_11_21-AM-10_49_07
Theory : core_2
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