Nuprl Lemma : radd-as-radd-list
∀[a,b:ℝ]. ((a + b) = radd-list([a; b]) ∈ ℝ)
Proof
Definitions occuring in Statement :
radd: a + b,
radd-list: radd-list(L),
real: ℝ,
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
radd-list: radd-list(L),
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
it: ⋅,
all: ∀x:A. B[x],
top: Top,
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
radd: a + b
Lemmas referenced :
valueall-type-has-valueall,
list_wf,
real_wf,
list-valueall-type,
real-valueall-type,
cons_wf,
nil_wf,
evalall-reduce,
valueall-type-real-list,
length_of_cons_lemma,
length_of_nil_lemma,
radd_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
hypothesisEquality,
callbyvalueReduce,
sqleReflexivity,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[a,b:\mBbbR{}]. ((a + b) = radd-list([a; b]))
Date html generated:
2016_05_18-AM-06_50_58
Last ObjectModification:
2015_12_28-AM-00_29_14
Theory : reals
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