Nuprl Lemma : req-rdiv2
∀x,y,z,u:ℝ. (z ≠ r0 ⇒ u ≠ r0 ⇒ ((x/u) = (y/z) ⇐⇒ (x * z) = (y * u)))
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rneq: x ≠ y,
req: x = y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
rdiv: (x/y),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
stable: Stable{P},
not: ¬A,
or: P ∨ Q,
false: False,
guard: {T}
Latex:
\mforall{}x,y,z,u:\mBbbR{}. (z \mneq{} r0 {}\mRightarrow{} u \mneq{} r0 {}\mRightarrow{} ((x/u) = (y/z) \mLeftarrow{}{}\mRightarrow{} (x * z) = (y * u)))
Date html generated:
2020_05_20-AM-11_00_11
Last ObjectModification:
2020_01_06-PM-00_26_43
Theory : reals
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