Nuprl Lemma : upper-bound_functionality
∀[A:Set(ℝ)]. ∀[b,c:ℝ]. {A ≤ c supposing A ≤ b} supposing b ≤ c
Proof
Definitions occuring in Statement :
upper-bound: A ≤ b
,
rset: Set(ℝ)
,
rleq: x ≤ y
,
real: ℝ
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
guard: {T}
Definitions unfolded in proof :
upper-bound: A ≤ b
,
guard: {T}
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
rev_uimplies: rev_uimplies(P;Q)
,
rge: x ≥ y
,
prop: ℙ
,
rleq: x ≤ y
,
rnonneg: rnonneg(x)
,
le: A ≤ B
,
and: P ∧ Q
Latex:
\mforall{}[A:Set(\mBbbR{})]. \mforall{}[b,c:\mBbbR{}]. \{A \mleq{} c supposing A \mleq{} b\} supposing b \mleq{} c
Date html generated:
2020_05_20-AM-11_27_41
Last ObjectModification:
2020_01_06-PM-00_19_44
Theory : reals
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