Nuprl Lemma : bar-base_subtype
∀[T:Type]. ((T + bar-base(T)) ⊆r bar-base(T))
Proof
Definitions occuring in Statement :
bar-base: bar-base(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bar-base: bar-base(T),
guard: {T},
subtype_rel: A ⊆r B
Lemmas referenced :
corec-ext,
continuous-monotone-union,
continuous-monotone-constant,
continuous-monotone-id,
ext-eq_inversion,
bar-base_wf,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
unionEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
axiomEquality
Latex:
\mforall{}[T:Type]. ((T + bar-base(T)) \msubseteq{}r bar-base(T))
Date html generated:
2016_05_14-AM-06_19_40
Last ObjectModification:
2015_12_26-PM-00_02_20
Theory : co-recursion
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