Nuprl Lemma : not_over_implies
∀[A,B:ℙ]. (¬(A ⇒ B) ⇐⇒ (¬¬A) ∧ (¬B))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
and_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
sqequalHypSubstitution,
hypothesis,
independent_functionElimination,
voidElimination,
hypothesisEquality,
lemma_by_obid,
isectElimination,
functionEquality,
productElimination,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:\mBbbP{}]. (\mneg{}(A {}\mRightarrow{} B) \mLeftarrow{}{}\mRightarrow{} (\mneg{}\mneg{}A) \mwedge{} (\mneg{}B))
Date html generated:
2016_05_13-PM-03_11_10
Last ObjectModification:
2016_01_06-PM-05_25_47
Theory : core_2
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