Nuprl Lemma : no-uniform-double-negation-elim
¬(∀[P:ℙ]. ((¬¬P) ⇒ P))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
false: False
Lemmas referenced :
double-negation-iff-xmiddle,
false_wf,
uall_wf,
not_wf,
no-uniform-xmiddle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
productElimination,
independent_functionElimination,
instantiate,
universeEquality,
lambdaEquality,
cumulativity,
functionEquality,
hypothesisEquality,
isect_memberFormation,
inlFormation,
voidElimination
Latex:
\mneg{}(\mforall{}[P:\mBbbP{}]. ((\mneg{}\mneg{}P) {}\mRightarrow{} P))
Date html generated:
2016_05_15-PM-03_19_12
Last ObjectModification:
2015_12_27-PM-01_03_32
Theory : general
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