Nuprl Lemma : rsub-int
∀[n:ℤ]. ∀m:ℤ. ((r(n) - r(m)) = r(n - m))
Proof
Definitions occuring in Statement :
rsub: x - y,
req: x = y,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
subtract: n - m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
rsub: x - y,
implies: P ⇒ Q,
true: True,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
subtract: n - m,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rsub_wf,
int-to-real_wf,
subtract_wf,
req_wf,
radd_wf,
rminus_wf,
req_weakening,
squash_wf,
true_wf,
minus-one-mul,
add-commutes,
minus-one-mul-top,
uiff_transitivity3,
real_wf,
rminus-int,
req_functionality,
radd-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
intEquality,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
extract_by_obid,
isectElimination,
hypothesis,
independent_functionElimination,
because_Cache,
minusEquality,
addEquality,
natural_numberEquality,
independent_isectElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality,
imageMemberEquality,
baseClosed,
productElimination
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}m:\mBbbZ{}. ((r(n) - r(m)) = r(n - m))
Date html generated:
2017_10_02-PM-07_17_31
Last ObjectModification:
2017_07_28-AM-07_21_10
Theory : reals
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