Nuprl Lemma : not_subtype_rel
∀[A,B:Type]. (¬A) ⊆r (¬B) supposing B ⊆r A
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
subtype_rel_dep_function,
false_wf,
subtype_rel_self,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
hypothesisEquality,
applyEquality,
lemma_by_obid,
isectElimination,
thin,
sqequalRule,
hypothesis,
independent_isectElimination,
lambdaFormation,
because_Cache,
functionEquality,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. (\mneg{}A) \msubseteq{}r (\mneg{}B) supposing B \msubseteq{}r A
Date html generated:
2016_05_15-PM-06_38_07
Last ObjectModification:
2015_12_27-AM-11_53_57
Theory : general
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