Nuprl Lemma : baseof_sq
∀[T:Type]. SQType(baseof(T))
Proof
Definitions occuring in Statement :
sq_type: SQType(T),
baseof: baseof(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
sq_type: SQType(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
baseof: baseof(T),
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
it_wf,
unit_wf,
base_wf,
equal_wf,
baseof_subtype_base,
baseof_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
hypothesis,
applyEquality,
lambdaEquality,
isectElimination,
inrEquality,
extract_by_obid,
equalityTransitivity,
equalitySymmetry,
isectEquality,
unionEquality,
hypothesisEquality,
thin,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
hyp_replacement,
applyLambdaEquality,
sqequalIntensionalEquality,
axiomSqEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. SQType(baseof(T))
Date html generated:
2019_06_20-AM-11_19_40
Last ObjectModification:
2018_08_21-PM-05_15_01
Theory : sqequal_1
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