Nuprl Definition : decreasing-on-interval
f[x] decreasing for x ∈ I == ∀x,y:{x:ℝ| x ∈ I} . ((x ≤ y) ⇒ (f[y] ≤ f[x]))
Definitions occuring in Statement :
i-member: r ∈ I,
rleq: x ≤ y,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]}
Definitions occuring in definition :
rleq: x ≤ y,
implies: P ⇒ Q,
i-member: r ∈ I,
real: ℝ,
set: {x:A| B[x]} ,
all: ∀x:A. B[x]
FDL editor aliases :
decreasing-on-interval
Latex:
f[x] decreasing for x \mmember{} I == \mforall{}x,y:\{x:\mBbbR{}| x \mmember{} I\} . ((x \mleq{} y) {}\mRightarrow{} (f[y] \mleq{} f[x]))
Date html generated:
2016_10_26-AM-11_35_25
Last ObjectModification:
2016_09_07-PM-06_53_01
Theory : reals
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