Nuprl Lemma : rless_complement
∀x,y:ℝ. (¬(x < y) ⇐⇒ y ≤ x)
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rless: x < y,
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
not: ¬A,
prop: ℙ,
false: False,
rev_implies: P ⇐ Q
Latex:
\mforall{}x,y:\mBbbR{}. (\mneg{}(x < y) \mLeftarrow{}{}\mRightarrow{} y \mleq{} x)
Date html generated:
2020_05_20-AM-10_56_57
Last ObjectModification:
2020_01_09-PM-01_39_43
Theory : reals
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