Nuprl Lemma : rv-congruent-trans
∀[n:ℕ]. ∀[a,b,p,q,r,s:ℝ^n]. (pq=rs) supposing (ab=rs and ab=pq)
Proof
Definitions occuring in Statement :
rv-congruent: ab=cd,
real-vec: ℝ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rv-congruent: ab=cd,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
req_inversion,
real-vec-dist_wf,
real_wf,
rleq_wf,
int-to-real_wf,
req_transitivity,
req_witness,
req_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
natural_numberEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b,p,q,r,s:\mBbbR{}\^{}n]. (pq=rs) supposing (ab=rs and ab=pq)
Date html generated:
2016_10_26-AM-10_28_21
Last ObjectModification:
2016_09_25-PM-02_10_33
Theory : reals
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