Nuprl Lemma : i-witness_wf
∀[I:Interval]. ∀[r:ℝ]. ∀[p:r ∈ I]. (i-witness(I;r;p) ∈ ℕ+)
Proof
Definitions occuring in Statement :
i-witness: i-witness(I;r;p),
i-member: r ∈ I,
interval: Interval,
real: ℝ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
top: Top,
uimplies: b supposing a,
exists: ∃x:A. B[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
i-witness: i-witness(I;r;p)
Lemmas referenced :
equal_wf,
pi1_wf_top,
subtype_rel_function,
i-approx_wf,
nat_plus_wf,
exists_wf,
i-member_wf,
real_wf,
all_wf,
interval_wf,
subtype_rel_self,
i-member-witness
Rules used in proof :
axiomEquality,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
voidEquality,
voidElimination,
isect_memberEquality,
independent_pairEquality,
productElimination,
lambdaFormation,
independent_isectElimination,
because_Cache,
hypothesisEquality,
lambdaEquality,
functionEquality,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
instantiate,
thin,
applyEquality,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[I:Interval]. \mforall{}[r:\mBbbR{}]. \mforall{}[p:r \mmember{} I]. (i-witness(I;r;p) \mmember{} \mBbbN{}\msupplus{})
Date html generated:
2018_05_22-PM-02_05_11
Last ObjectModification:
2018_05_21-AM-00_18_02
Theory : reals
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