Nuprl Lemma : i-real_wf
∀[I:Interval]. ∀[p:i-type(I)]. (real(p) ∈ ℝ)
Proof
Definitions occuring in Statement :
i-real: real(p),
i-type: i-type(I),
interval: Interval,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
i-real: real(p),
i-type: i-type(I),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
pi2_wf,
nat_plus_wf,
real_wf,
i-member_wf,
i-approx_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setEquality,
hypothesisEquality,
applyEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[p:i-type(I)]. (real(p) \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-08_44_50
Last ObjectModification:
2015_12_27-PM-11_49_00
Theory : reals
Home
Index