Nuprl Lemma : radd_wf
∀[a,b:ℝ]. (a + b ∈ ℝ)
Proof
Definitions occuring in Statement :
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
radd: a + b,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
length_wf,
regular-int-seq_wf,
nat_plus_wf,
length_of_nil_lemma,
length_of_cons_lemma,
nil_wf,
real_wf,
cons_wf,
reg-seq-list-add_wf,
less_than_wf,
accelerate_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
hypothesis,
because_Cache,
applyEquality,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setEquality,
functionEquality,
intEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b:\mBbbR{}]. (a + b \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-06_48_39
Last ObjectModification:
2016_01_17-AM-01_45_24
Theory : reals
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