Nuprl Lemma : interval-retraction_functionality
∀[u,v,x,u',v',x':ℝ].
(interval-retraction(u;v;x) = interval-retraction(u';v';x')) supposing ((x = x') and (v = v') and (u = u'))
Proof
Definitions occuring in Statement :
interval-retraction: interval-retraction(u;v;r),
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
interval-retraction: interval-retraction(u;v;r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rmin_wf,
rmax_wf,
req_wf,
real_wf,
req_weakening,
req_functionality,
rmin_functionality,
rmax_functionality
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[u,v,x,u',v',x':\mBbbR{}].
(interval-retraction(u;v;x) = interval-retraction(u';v';x')) supposing
((x = x') and
(v = v') and
(u = u'))
Date html generated:
2017_10_03-AM-10_05_23
Last ObjectModification:
2017_07_10-PM-05_12_31
Theory : reals
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