Nuprl Lemma : classical-double-negation
∀P:ℙ. {¬¬P ⇐⇒ P}
Proof
Definitions occuring in Statement :
classical: {P},
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
classical: {P},
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
false_wf,
not_wf,
iff_wf,
it_wf,
classical-excluded-middle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
universeEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
introduction,
setElimination,
rename,
dependent_set_memberEquality,
hypothesis,
isectElimination,
unionElimination,
independent_pairFormation,
lambdaEquality,
independent_functionElimination,
voidElimination,
functionEquality,
sqequalRule
Latex:
\mforall{}P:\mBbbP{}. \{\mneg{}\mneg{}P \mLeftarrow{}{}\mRightarrow{} P\}
Date html generated:
2016_05_13-PM-03_16_37
Last ObjectModification:
2016_01_06-PM-05_20_46
Theory : core_2
Home
Index