Nuprl Lemma : stable__from_decidable
∀[P:ℙ]. (Dec(P) ⇒ Stable{P})
Proof
Definitions occuring in Statement :
stable: Stable{P},
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Definitions unfolded in proof :
stable: Stable{P},
decidable: Dec(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
false: False,
prop: ℙ,
or: P ∨ Q
Lemmas referenced :
not_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
hypothesis,
rename,
Error :universeIsType,
universeEquality,
unionElimination,
independent_functionElimination
Latex:
\mforall{}[P:\mBbbP{}]. (Dec(P) {}\mRightarrow{} Stable\{P\})
Date html generated:
2019_06_20-AM-11_15_13
Last ObjectModification:
2018_09_26-AM-10_43_15
Theory : core_2
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