Nuprl Lemma : rv-congruent_wf
∀[n:ℕ]. ∀[a,b,c,d:ℝ^n]. (ab=cd ∈ ℙ)
Proof
Definitions occuring in Statement :
rv-congruent: ab=cd,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rv-congruent: ab=cd,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
req_wf,
real-vec-dist_wf,
real_wf,
rleq_wf,
int-to-real_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
natural_numberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b,c,d:\mBbbR{}\^{}n]. (ab=cd \mmember{} \mBbbP{})
Date html generated:
2016_10_26-AM-10_27_52
Last ObjectModification:
2016_09_25-PM-01_02_22
Theory : reals
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