Nuprl Lemma : rv-congruent-implies-eq
∀n:ℕ. ∀a,b,c:ℝ^n. (aa=bc
⇒ req-vec(n;b;c))
Proof
Definitions occuring in Statement :
rv-congruent: ab=cd
,
req-vec: req-vec(n;x;y)
,
real-vec: ℝ^n
,
nat: ℕ
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
Definitions unfolded in proof :
rv-congruent: ab=cd
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
prop: ℙ
,
subtype_rel: A ⊆r B
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
guard: {T}
Lemmas referenced :
real-vec-dist-same-zero,
req_wf,
real-vec-dist_wf,
real_wf,
rleq_wf,
int-to-real_wf,
real-vec_wf,
nat_wf,
real-vec-dist-identity,
req_inversion,
req_functionality,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
natural_numberEquality,
because_Cache,
productElimination,
independent_isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b,c:\mBbbR{}\^{}n. (aa=bc {}\mRightarrow{} req-vec(n;b;c))
Date html generated:
2017_10_03-AM-11_04_08
Last ObjectModification:
2017_08_11-PM-06_33_15
Theory : reals
Home
Index