Nuprl Lemma : rsub_functionality
∀[x1,x2,y1,y2:ℝ]. ((x1 - y1) = (x2 - y2)) supposing ((y1 = y2) and (x1 = x2))
Proof
Definitions occuring in Statement :
rsub: x - y,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rsub: x - y,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rsub_wf,
req_wf,
real_wf,
radd_wf,
rminus_wf,
req_weakening,
req_functionality,
radd_functionality,
rminus_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x1,x2,y1,y2:\mBbbR{}]. ((x1 - y1) = (x2 - y2)) supposing ((y1 = y2) and (x1 = x2))
Date html generated:
2016_05_18-AM-06_55_09
Last ObjectModification:
2015_12_28-AM-00_31_35
Theory : reals
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