Nuprl Lemma : ratreal-ratsub
∀[a,b:ℤ × ℕ+]. (ratreal(ratsub(a;b)) = (ratreal(a) - ratreal(b)))
Proof
Definitions occuring in Statement :
ratsub: ratsub(x;y),
ratreal: ratreal(r),
rsub: x - y,
req: x = y,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
squash: ↓T
Lemmas referenced :
sq_stable__req,
ratreal_wf,
ratsub_wf,
rsub_wf,
istype-int,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
independent_functionElimination,
lambdaFormation_alt,
because_Cache,
imageMemberEquality,
baseClosed,
imageElimination,
equalityIstype,
dependent_functionElimination,
productIsType,
universeIsType
Latex:
\mforall{}[a,b:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}]. (ratreal(ratsub(a;b)) = (ratreal(a) - ratreal(b)))
Date html generated:
2019_10_30-AM-09_25_54
Last ObjectModification:
2019_01_11-PM-00_24_49
Theory : reals
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