Nuprl Lemma : sq_stable__rneq-or
∀x,y:ℝ. SqStable(x ≠ r0 ∨ y ≠ r0)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
int-to-real: r(n),
real: ℝ,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
or: P ∨ Q,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
rneq-zero-or: rneq-zero-or(x;y),
sqs-rneq-or,
decidable__lt,
any: any x,
decidable__squash,
decidable__and,
decidable__less_than',
decidable_functionality,
squash_elim,
sq_stable_from_decidable,
iff_preserves_decidability,
sq_stable__from_stable,
stable__from_decidable,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
sqs-rneq-or,
lifting-strict-decide,
istype-void,
strict4-decide,
lifting-strict-less,
decidable__lt,
decidable__squash,
decidable__and,
decidable__less_than',
decidable_functionality,
squash_elim,
sq_stable_from_decidable,
iff_preserves_decidability,
sq_stable__from_stable,
stable__from_decidable
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality_alt,
voidElimination,
independent_isectElimination
Latex:
\mforall{}x,y:\mBbbR{}. SqStable(x \mneq{} r0 \mvee{} y \mneq{} r0)
Date html generated:
2019_10_29-AM-09_36_14
Last ObjectModification:
2019_01_09-PM-05_22_16
Theory : reals
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