Nuprl Lemma : rmin-req-rminus-rmax
∀[x,y:ℝ]. (rmin(x;y) = -(rmax(-(x);-(y))))
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
rmax: rmax(x;y),
req: x = y,
rminus: -(x),
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rmin_wf,
rminus_wf,
rmax_wf,
real_wf,
req_weakening,
req_functionality,
req_transitivity,
rminus-rmax,
rmin_functionality,
rminus-rminus
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,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. (rmin(x;y) = -(rmax(-(x);-(y))))
Date html generated:
2016_05_18-AM-06_59_38
Last ObjectModification:
2015_12_28-AM-00_32_43
Theory : reals
Home
Index