Nuprl Lemma : rneq-zero-or_wf
∀[x,y:ℝ]. rneq-zero-or(x;y) ∈ x ≠ r0 ∨ y ≠ r0 supposing x ≠ r0 ∨ y ≠ r0
Proof
Definitions occuring in Statement :
rneq-zero-or: rneq-zero-or(x;y),
rneq: x ≠ y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
sq_stable__rneq-or,
sq_stable: SqStable(P),
squash: ↓T,
implies: P ⇒ Q
Lemmas referenced :
rneq_wf,
int-to-real_wf,
real_wf,
sq_stable__rneq-or,
subtype_rel_self,
sq_stable_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionIsType,
universeIsType,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
applyEquality,
instantiate,
functionEquality,
unionEquality,
imageMemberEquality,
baseClosed,
rename,
functionExtensionality
Latex:
\mforall{}[x,y:\mBbbR{}]. rneq-zero-or(x;y) \mmember{} x \mneq{} r0 \mvee{} y \mneq{} r0 supposing x \mneq{} r0 \mvee{} y \mneq{} r0
Date html generated:
2019_10_29-AM-09_36_22
Last ObjectModification:
2019_01_09-PM-05_24_47
Theory : reals
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