Nuprl Lemma : square-nonzero
∀x:ℝ. (x * x ≠ r0 ⇐⇒ x ≠ r0)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q
Lemmas referenced :
rneq_wf,
rmul_wf,
int-to-real_wf,
rmul-neq-zero,
real_wf,
rmul-nonzero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
productElimination
Latex:
\mforall{}x:\mBbbR{}. (x * x \mneq{} r0 \mLeftarrow{}{}\mRightarrow{} x \mneq{} r0)
Date html generated:
2016_10_26-AM-09_13_54
Last ObjectModification:
2016_09_06-PM-03_05_44
Theory : reals
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