Nuprl Lemma : rv-ge_wf
∀[n:ℕ]. ∀[c,d,a,b:ℝ^n]. (cd ≥ ab ∈ ℙ)
Proof
Definitions occuring in Statement :
rv-ge: cd ≥ ab,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
rv-ge: cd ≥ ab,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_wf,
rv-congruent_wf,
rv-between_wf,
real-vec-sep_wf,
real-vec_wf,
exists_wf,
not_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
because_Cache,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[c,d,a,b:\mBbbR{}\^{}n]. (cd \mgeq{} ab \mmember{} \mBbbP{})
Date html generated:
2016_10_28-AM-07_37_35
Last ObjectModification:
2016_10_27-PM-01_23_09
Theory : reals
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