Nuprl Lemma : DNS-iff-not-not-GMP
∀[A:ℕ ⟶ ℙ]. (DNSi.A[i] ⇐⇒ ¬¬GMPi.A[i]))
Proof
Definitions occuring in Statement :
generalized-markov-principle: GMPi.A[i]),
double-negation-shift: DNSi.A[i],
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
not: ¬A,
function: x:A ⟶ B[x]
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
double-negation-shift: DNSi.A[i],
generalized-markov-principle: GMPi.A[i]),
exists: ∃x:A. B[x],
guard: {T}
Lemmas referenced :
not_wf,
generalized-markov-principle_wf,
nat_wf,
double-negation-shift_wf,
all_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
lemma_by_obid,
isectElimination,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
functionEquality,
cumulativity,
universeEquality,
dependent_pairFormation
Latex:
\mforall{}[A:\mBbbN{} {}\mrightarrow{} \mBbbP{}]. (DNSi.A[i] \mLeftarrow{}{}\mRightarrow{} \mneg{}\mneg{}GMPi.A[i]))
Date html generated:
2016_05_15-PM-03_20_51
Last ObjectModification:
2015_12_27-PM-01_04_21
Theory : general
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