Nuprl Lemma : sq-all-large_wf
∀[P:ℕ ⟶ ℙ]. (∀large(n).{P[n]} ∈ ℙ)
Proof
Definitions occuring in Statement :
sq-all-large: ∀large(n).{P[n]},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq-all-large: ∀large(n).{P[n]},
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
sq_exists_wf,
nat_wf,
all_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
functionEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality
Latex:
\mforall{}[P:\mBbbN{} {}\mrightarrow{} \mBbbP{}]. (\mforall{}large(n).\{P[n]\} \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-05_29_52
Last ObjectModification:
2015_12_27-PM-02_11_07
Theory : general
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