Nuprl Lemma : radd-bdd-diff
∀a,b:ℝ. bdd-diff(a + b;λn.((a n) + (b n)))
Proof
Definitions occuring in Statement :
radd: a + b,
real: ℝ,
bdd-diff: bdd-diff(f;g),
all: ∀x:A. B[x],
apply: f a,
lambda: λx.A[x],
add: n + m
Definitions unfolded in proof :
all: ∀x:A. B[x],
radd: a + b,
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
top: Top,
real: ℝ,
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
false: False,
not: ¬A,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
absval: |i|,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
guard: {T},
subtract: n - m
Lemmas referenced :
zero-mul,
add-mul-special,
add-swap,
zero-add,
minus-one-mul,
minus-add,
add-associates,
iff_weakening_equal,
reg-seq-list-add-as-l_sum,
true_wf,
squash_wf,
bdd-diff_weakening,
accelerate-bdd-diff,
bdd-diff_functionality,
nat_wf,
l_sum_nil_lemma,
l_sum_cons_lemma,
map_nil_lemma,
map_cons_lemma,
subtract_wf,
absval_wf,
all_wf,
le_wf,
false_wf,
length_wf,
regular-int-seq_wf,
nat_plus_wf,
length_of_nil_lemma,
length_of_cons_lemma,
nil_wf,
cons_wf,
reg-seq-list-add_wf,
less_than_wf,
accelerate_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
introduction,
imageMemberEquality,
hypothesisEquality,
baseClosed,
because_Cache,
applyEquality,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setEquality,
functionEquality,
intEquality,
setElimination,
rename,
addEquality,
dependent_pairFormation,
multiplyEquality,
minusEquality,
independent_functionElimination,
productElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_isectElimination
Latex:
\mforall{}a,b:\mBbbR{}. bdd-diff(a + b;\mlambda{}n.((a n) + (b n)))
Date html generated:
2016_05_18-AM-06_48_42
Last ObjectModification:
2016_01_17-AM-01_45_33
Theory : reals
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