Nuprl Lemma : top-subtype-function
∀[A,B:Type]. Top ⊆r (A ⟶ B) supposing ¬A
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
top_wf,
not_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
isect_memberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
axiomEquality,
sqequalRule,
hypothesis,
lemma_by_obid,
lambdaEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
functionExtensionality,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[A,B:Type]. Top \msubseteq{}r (A {}\mrightarrow{} B) supposing \mneg{}A
Date html generated:
2019_06_20-PM-00_27_47
Last ObjectModification:
2018_08_02-AM-11_27_46
Theory : subtype_1
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