Nuprl Lemma : weakly-infinite_wf
∀[S:ℕ ⟶ ℙ]. (w∃∞x.S[x] ∈ ℙ)
Proof
Definitions occuring in Statement :
weakly-infinite: w∃∞p.S[p],
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,
weakly-infinite: w∃∞p.S[p],
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
all_wf,
nat_wf,
not_wf,
exists_wf,
and_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[S:\mBbbN{} {}\mrightarrow{} \mBbbP{}]. (w\mexists{}\minfty{}x.S[x] \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_49_52
Last ObjectModification:
2015_12_26-AM-10_17_39
Theory : bar-induction
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