Nuprl Lemma : real-vec-dist-sub-zero
∀[n:ℕ]. ∀[p,q:ℝ^n]. (d(p - q;λi.r0) = d(p;q))
Proof
Definitions occuring in Statement :
real-vec-dist: d(x;y),
real-vec-sub: X - Y,
real-vec: ℝ^n,
req: x = y,
int-to-real: r(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec: ℝ^n,
nat: ℕ,
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
real-vec-sub: X - Y,
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
req_witness,
real-vec-dist_wf,
real-vec-sub_wf,
int-to-real_wf,
int_seg_wf,
real_wf,
rleq_wf,
real-vec_wf,
nat_wf,
real-vec-dist-translation,
req_functionality,
req_weakening,
req_inversion,
real-vec-dist_functionality,
req-vec_weakening,
rsub_wf,
itermSubtract_wf,
itermConstant_wf,
itermVar_wf,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
applyEquality,
setEquality,
independent_functionElimination,
isect_memberEquality,
independent_isectElimination,
productElimination,
lambdaFormation,
dependent_functionElimination,
approximateComputation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p,q:\mBbbR{}\^{}n]. (d(p - q;\mlambda{}i.r0) = d(p;q))
Date html generated:
2018_05_22-PM-02_25_27
Last ObjectModification:
2018_03_23-AM-10_47_52
Theory : reals
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