Nuprl Lemma : double-negation-shift_wf
∀A:ℕ ⟶ ℙ. (DNSi.A[i] ∈ ℙ)
Proof
Definitions occuring in Statement :
double-negation-shift: DNSi.A[i],
nat: ℕ,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
double-negation-shift: DNSi.A[i],
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
applyEquality,
hypothesisEquality,
cumulativity,
universeEquality
Latex:
\mforall{}A:\mBbbN{} {}\mrightarrow{} \mBbbP{}. (DNSi.A[i] \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_20_43
Last ObjectModification:
2015_12_27-PM-01_04_00
Theory : general
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