Nuprl Lemma : rmin-req
∀[x,y:ℝ]. rmin(x;y) = y supposing y ≤ x
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rmin: rmin(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,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q
Lemmas referenced :
rmin-req-rminus-rmax,
req_inversion,
iff_weakening_equal,
rminus-rminus-eq,
true_wf,
squash_wf,
req_wf,
rminus_functionality,
req_functionality,
req_weakening,
rmax_wf,
real_wf,
rleq_wf,
rmin_wf,
req_witness,
rminus-reverses-rleq,
rminus_wf,
rmax-req
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
applyEquality,
lambdaEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. rmin(x;y) = y supposing y \mleq{} x
Date html generated:
2016_05_18-AM-07_15_43
Last ObjectModification:
2016_01_17-AM-01_53_44
Theory : reals
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