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
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