Nuprl Lemma : ravg_wf
∀[x,y:ℝ]. (ravg(x;y) ∈ ℝ)
Proof
Definitions occuring in Statement :
ravg: ravg(x;y),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ravg: ravg(x;y),
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ
Lemmas referenced :
real_wf,
rless_wf,
rless-int,
int-to-real_wf,
radd_wf,
rdiv_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. (ravg(x;y) \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-07_34_52
Last ObjectModification:
2016_01_17-AM-02_01_49
Theory : reals
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