Nuprl Lemma : real-vec-add-cancel
∀[n:ℕ]. ∀[p,a,b:ℝ^n]. req-vec(n;a;b) supposing req-vec(n;p + a;p + b)
Proof
Definitions occuring in Statement :
real-vec-add: X + Y,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
real-vec-add: X + Y,
real-vec: ℝ^n,
nat: ℕ,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
req-implies-req,
radd_wf,
int_seg_wf,
req_witness,
req-vec_wf,
real-vec-add_wf,
real-vec_wf,
nat_wf,
rsub_wf,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
req-iff-rsub-is-0,
real_polynomial_null,
int-to-real_wf,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
extract_by_obid,
isectElimination,
applyEquality,
because_Cache,
independent_isectElimination,
natural_numberEquality,
setElimination,
rename,
lambdaEquality,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
approximateComputation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p,a,b:\mBbbR{}\^{}n]. req-vec(n;a;b) supposing req-vec(n;p + a;p + b)
Date html generated:
2018_05_22-PM-02_25_10
Last ObjectModification:
2018_03_23-AM-10_57_09
Theory : reals
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