Nuprl Lemma : rabs-int-rmul
∀[k:ℤ]. ∀[x:ℝ]. (|k * x| = |k| * |x|)
Proof
Definitions occuring in Statement :
rabs: |x|,
int-rmul: k1 * a,
req: x = y,
real: ℝ,
absval: |i|,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
true: True,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rabs_wf,
int-rmul_wf,
absval_wf,
nat_wf,
real_wf,
req_wf,
rmul_wf,
int-to-real_wf,
req_weakening,
uiff_transitivity2,
uiff_transitivity,
req_functionality,
rabs_functionality,
int-rmul-req,
rabs-rmul,
squash_wf,
true_wf,
rabs-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
independent_functionElimination,
isect_memberEquality,
because_Cache,
intEquality,
natural_numberEquality,
independent_isectElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
productElimination
Latex:
\mforall{}[k:\mBbbZ{}]. \mforall{}[x:\mBbbR{}]. (|k * x| = |k| * |x|)
Date html generated:
2016_10_26-AM-09_08_10
Last ObjectModification:
2016_08_28-PM-02_36_52
Theory : reals
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