Nuprl Lemma : baseof_subtype_base
∀[T:Type]. (baseof(T) ⊆r Base)
Proof
Definitions occuring in Statement :
baseof: baseof(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
baseof: baseof(T),
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
isect_subtype_base,
unit_wf,
base_wf,
equal_wf,
it_wf,
subtype_rel_self,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesis,
lambdaEquality,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaFormation,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination,
dependent_pairFormation,
inrEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. (baseof(T) \msubseteq{}r Base)
Date html generated:
2019_06_20-AM-11_19_30
Last ObjectModification:
2018_08_21-PM-01_52_34
Theory : subtype_0
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