Nuprl Lemma : rn-metric-msep
∀n:ℕ. ∀x,y:ℝ^n. (x # y ⇐⇒ x ≠ y)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
rn-metric: rn-metric(n),
real-vec: ℝ^n,
msep: x # y,
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
msep: x # y,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
real-vec: ℝ^n,
prop: ℙ,
rev_implies: P ⇐ Q
Latex:
\mforall{}n:\mBbbN{}. \mforall{}x,y:\mBbbR{}\^{}n. (x \# y \mLeftarrow{}{}\mRightarrow{} x \mneq{} y)
Date html generated:
2020_05_20-PM-00_45_26
Last ObjectModification:
2019_11_11-PM-04_00_11
Theory : reals
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