Nuprl Lemma : real-vec-mul_functionality
∀[n:ℕ]. ∀[X,Y:ℝ^n]. ∀[a,b:ℝ]. (req-vec(n;a*X;b*Y)) supposing ((a = b) and req-vec(n;X;Y))
Proof
Definitions occuring in Statement :
real-vec-mul: a*X,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
req: x = y,
real: ℝ,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
real-vec-mul: a*X,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
int_seg_wf,
req_witness,
rmul_wf,
req_wf,
all_wf,
real_wf,
nat_wf,
req_weakening,
req_functionality,
rmul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
applyEquality,
functionExtensionality,
because_Cache,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
independent_isectElimination,
productElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[X,Y:\mBbbR{}\^{}n]. \mforall{}[a,b:\mBbbR{}]. (req-vec(n;a*X;b*Y)) supposing ((a = b) and req-vec(n;X;Y))
Date html generated:
2016_10_26-AM-10_17_04
Last ObjectModification:
2016_09_24-PM-09_24_24
Theory : reals
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