Nuprl Lemma : not_over_and_b

∀[A,B:ℙ].  ¬(A ∧ B) supposing (¬A) ∨ (¬B)


Proof




Definitions occuring in Statement :  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  prop: ℙ,  not: ¬A,  or: P ∨ Q,  and: P ∧ Q
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  uimplies: b supposing a,  not: ¬A,  implies: P ⇒ Q,  false: False,  or: P ∨ Q,  and: P ∧ Q,  prop: ℙ
Lemmas referenced :  not_wf,  or_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  Error :isect_memberFormation_alt,  introduction,  cut,  lambdaFormation,  thin,  sqequalHypSubstitution,  unionElimination,  productElimination,  independent_functionElimination,  hypothesis,  voidElimination,  productEquality,  cumulativity,  hypothesisEquality,  sqequalRule,  lambdaEquality,  dependent_functionElimination,  because_Cache,  Error :unionIsType,  Error :universeIsType,  extract_by_obid,  isectElimination,  isect_memberEquality,  equalityTransitivity,  equalitySymmetry,  Error :inhabitedIsType,  universeEquality

Latex:
\mforall{}[A,B:\mBbbP{}].    \mneg{}(A  \mwedge{}  B)  supposing  (\mneg{}A)  \mvee{}  (\mneg{}B)



Date html generated: 2019_06_20-AM-11_16_06
Last ObjectModification: 2018_09_26-AM-10_24_01

Theory : core_2


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