Nuprl Lemma : rabs-rneq
∀a,b:ℝ. (|a| ≠ |b| ⇒ a ≠ b)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rabs: |x|,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
rneq: x ≠ y,
or: P ∨ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
guard: {T},
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Latex:
\mforall{}a,b:\mBbbR{}. (|a| \mneq{} |b| {}\mRightarrow{} a \mneq{} b)
Date html generated:
2020_05_20-AM-11_03_16
Last ObjectModification:
2019_11_11-PM-09_13_28
Theory : reals
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