Nuprl Lemma : real-vec-add-com
∀[n:ℕ]. ∀[X,Y:ℝ^n]. req-vec(n;X + Y;Y + X)
Proof
Definitions occuring in Statement :
real-vec-add: X + Y,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
real-vec-add: X + Y,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q
Lemmas referenced :
radd_comm,
int_seg_wf,
req_witness,
radd_wf,
real_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
functionExtensionality,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
hypothesis,
because_Cache,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[X,Y:\mBbbR{}\^{}n]. req-vec(n;X + Y;Y + X)
Date html generated:
2016_10_26-AM-10_15_28
Last ObjectModification:
2016_09_24-PM-09_12_53
Theory : reals
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