Nuprl Lemma : rmin_lb
∀[x,y,z:ℝ]. rmin(x;y) ≤ z supposing (x ≤ z) ∨ (y ≤ z)
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rmin: rmin(x;y),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
or: P ∨ Q,
and: P ∧ Q,
guard: {T},
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ
Lemmas referenced :
rmin-rleq,
rleq_transitivity,
rmin_wf,
less_than'_wf,
rsub_wf,
real_wf,
nat_plus_wf,
or_wf,
rleq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
unionElimination,
productElimination,
hypothesis,
independent_isectElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
because_Cache,
applyEquality,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[x,y,z:\mBbbR{}]. rmin(x;y) \mleq{} z supposing (x \mleq{} z) \mvee{} (y \mleq{} z)
Date html generated:
2016_05_18-AM-07_16_55
Last ObjectModification:
2015_12_28-AM-00_44_03
Theory : reals
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