Nuprl Lemma : rabs*_functionality
∀[x,y:ℝ*]. (x = y ⇒ |x| = |y|)
Proof
Definitions occuring in Statement :
rabs*: |x|,
req*: x = y,
real*: ℝ*,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rabs*: |x|,
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
rfun*_functionality,
rabs_wf,
real_wf,
req_witness,
req_wf,
req*_wf,
real*_wf,
req_weakening,
req_functionality,
rabs_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}*]. (x = y {}\mRightarrow{} |x| = |y|)
Date html generated:
2018_05_22-PM-03_15_25
Last ObjectModification:
2017_10_06-PM-03_45_33
Theory : reals_2
Home
Index