Nuprl Lemma : rabs-rminus
∀[x:ℝ]. (|-(x)| = |x| ∈ ℝ)
Proof
Definitions occuring in Statement :
rabs: |x|,
rminus: -(x),
real: ℝ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
real: ℝ,
member: t ∈ T,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
nat: ℕ,
subtype_rel: A ⊆r B,
rminus: -(x),
rabs: |x|
Lemmas referenced :
real-regular,
rabs_wf,
rminus_wf,
less_than_wf,
regular-int-seq_wf,
iff_weakening_equal,
absval-minus,
true_wf,
squash_wf,
equal_wf,
nat_wf,
absval_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
baseClosed,
because_Cache,
independent_functionElimination,
productElimination,
independent_isectElimination,
universeEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
lambdaEquality,
rename,
setElimination,
applyEquality,
intEquality,
functionExtensionality
Latex:
\mforall{}[x:\mBbbR{}]. (|-(x)| = |x|)
Date html generated:
2017_10_03-AM-08_22_57
Last ObjectModification:
2017_09_20-PM-05_36_35
Theory : reals
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