Nuprl Lemma : Sierpinski-cases2
∀[x:Sierpinski]. (¬¬((x = ⊤ ∈ Sierpinski) ∨ (x = ⊥ ∈ Sierpinski)))
Proof
Definitions occuring in Statement :
Sierpinski: Sierpinski,
Sierpinski-top: ⊤,
Sierpinski-bottom: ⊥,
uall: ∀[x:A]. B[x],
not: ¬A,
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
false: False
Lemmas referenced :
Sierpinski-cases,
equal_wf,
Sierpinski_wf,
Sierpinski-bottom_wf,
Sierpinski-top_wf,
not_wf,
or_wf,
subtype-Sierpinski
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
introduction,
independent_functionElimination,
inlFormation,
applyEquality,
because_Cache,
sqequalRule,
independent_pairFormation,
inrFormation,
voidElimination
Latex:
\mforall{}[x:Sierpinski]. (\mneg{}\mneg{}((x = \mtop{}) \mvee{} (x = \mbot{})))
Date html generated:
2019_10_31-AM-06_35_36
Last ObjectModification:
2015_12_28-AM-11_21_49
Theory : synthetic!topology
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