Nuprl Lemma : stable__and
∀[P,Q:ℙ]. (Stable{P} ⇒ Stable{Q} ⇒ Stable{P ∧ Q})
Proof
Definitions occuring in Statement :
stable: Stable{P},
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
and: P ∧ Q,
prop: ℙ,
false: False,
not: ¬A,
member: t ∈ T,
uimplies: b supposing a,
stable: Stable{P},
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
stable_wf,
not_wf
Rules used in proof :
productElimination,
independent_functionElimination,
independent_isectElimination,
universeEquality,
independent_pairFormation,
rename,
hypothesis,
cumulativity,
productEquality,
isectElimination,
extract_by_obid,
voidElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
introduction,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[P,Q:\mBbbP{}]. (Stable\{P\} {}\mRightarrow{} Stable\{Q\} {}\mRightarrow{} Stable\{P \mwedge{} Q\})
Date html generated:
2016_10_21-AM-09_34_53
Last ObjectModification:
2016_09_26-PM-00_40_12
Theory : core_2
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