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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