Nuprl Lemma : rabs-abs
∀[a:ℤ]. (|r(a)| = r(|a|))
Proof
Definitions occuring in Statement :
rabs: |x|,
req: x = y,
int-to-real: r(n),
absval: |i|,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nat: ℕ
Lemmas referenced :
nat_wf,
rabs_wf,
req_witness,
req_weakening,
iff_weakening_equal,
absval_wf,
int-to-real_wf,
rabs-int,
real_wf,
true_wf,
squash_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
sqequalRule,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
setElimination,
rename,
intEquality
Latex:
\mforall{}[a:\mBbbZ{}]. (|r(a)| = r(|a|))
Date html generated:
2016_05_18-AM-07_14_02
Last ObjectModification:
2016_01_17-AM-01_53_33
Theory : reals
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