Nuprl Lemma : rminus-neq-zero
∀x:ℝ. (x ≠ r0 ⇒ -(x) ≠ r0)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False
Latex:
\mforall{}x:\mBbbR{}. (x \mneq{} r0 {}\mRightarrow{} -(x) \mneq{} r0)
Date html generated:
2020_05_20-AM-10_57_30
Last ObjectModification:
2020_01_09-PM-04_36_01
Theory : reals
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