Nuprl Lemma : xmiddle-implies-stable
XM ⇒ (∀P:ℙ. Stable{P})
Proof
Definitions occuring in Statement :
xmiddle: XM,
stable: Stable{P},
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
xmiddle: XM,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
stable: Stable{P},
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ
Lemmas referenced :
not_wf,
xmiddle_wf
Rules used in proof :
unionElimination,
independent_functionElimination,
Error :isect_memberFormation_alt,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
isectElimination,
rename,
Error :universeIsType,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
universeEquality,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
XM {}\mRightarrow{} (\mforall{}P:\mBbbP{}. Stable\{P\})
Date html generated:
2019_06_20-PM-01_04_11
Last ObjectModification:
2019_06_20-PM-01_02_05
Theory : core_2
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