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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