Nuprl Lemma : Sierpinski-cases
∀[x:Sierpinski]. (¬((¬(x = ⊤ ∈ Sierpinski)) ∧ (¬(x = ⊥ ∈ Sierpinski))))
Proof
Definitions occuring in Statement :
Sierpinski: Sierpinski,
Sierpinski-top: ⊤,
Sierpinski-bottom: ⊥,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
not-Sierpinski-top,
and_wf,
not_wf,
equal_wf,
Sierpinski_wf,
Sierpinski-top_wf,
subtype-Sierpinski,
Sierpinski-bottom_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
voidElimination,
because_Cache,
applyEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination
Latex:
\mforall{}[x:Sierpinski]. (\mneg{}((\mneg{}(x = \mtop{})) \mwedge{} (\mneg{}(x = \mbot{}))))
Date html generated:
2019_10_31-AM-06_35_34
Last ObjectModification:
2015_12_28-AM-11_21_46
Theory : synthetic!topology
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