Nuprl Lemma : req-iff-bdd-diff
∀[x,y:ℝ]. uiff(x = y;bdd-diff(x;y))
Proof
Definitions occuring in Statement :
req: x = y,
real: ℝ,
bdd-diff: bdd-diff(f;g),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
req: x = y,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
real: ℝ,
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
nat_plus: ℕ+,
less_than: a < b,
true: True,
guard: {T}
Lemmas referenced :
bdd-diff-regular,
less_than_wf,
real_wf,
bdd-diff_wf,
sq_stable__le,
all_wf,
le_wf,
false_wf,
nat_plus_wf,
nat_wf,
subtract_wf,
absval_wf,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
independent_pairFormation,
cut,
introduction,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
voidElimination,
lemma_by_obid,
isectElimination,
natural_numberEquality,
applyEquality,
setElimination,
rename,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
dependent_set_memberEquality,
lambdaFormation,
because_Cache,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
independent_isectElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. uiff(x = y;bdd-diff(x;y))
Date html generated:
2016_05_18-AM-06_50_18
Last ObjectModification:
2016_01_17-AM-01_45_50
Theory : reals
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