Nuprl Lemma : radd*_functionality
∀[x,y,u,v:ℝ*]. (x = y ⇒ u = v ⇒ x + u = y + v)
Proof
Definitions occuring in Statement :
radd*: x + y,
req*: x = y,
real*: ℝ*,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
member: t ∈ T,
radd*: x + y,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
radd_functionality,
req_functionality,
req*_weakening,
rfun*2_functionality,
req*_functionality,
req_weakening,
req_wf,
req_witness,
real_wf,
radd_wf,
rfun*2_wf,
real*_wf,
req*_wf
Rules used in proof :
independent_isectElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
productEquality,
independent_functionElimination,
sqequalRule,
productElimination,
lambdaEquality,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x,y,u,v:\mBbbR{}*]. (x = y {}\mRightarrow{} u = v {}\mRightarrow{} x + u = y + v)
Date html generated:
2018_05_22-PM-03_16_06
Last ObjectModification:
2018_05_21-AM-00_00_47
Theory : reals_2
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