Nuprl Lemma : minimal-triple-neg
∀[E:Type]. ∀[A:ℙ]. (((A ⇒ E) ⇒ E) ⇒ E ⇐⇒ A ⇒ E)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
thin,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality
Latex:
\mforall{}[E:Type]. \mforall{}[A:\mBbbP{}]. (((A {}\mRightarrow{} E) {}\mRightarrow{} E) {}\mRightarrow{} E \mLeftarrow{}{}\mRightarrow{} A {}\mRightarrow{} E)
Date html generated:
2018_05_21-PM-00_00_21
Last ObjectModification:
2018_02_09-AM-10_46_07
Theory : core_2
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