Nuprl Lemma : rat-rleq-cases-ext
∀x,y:ℤ × ℕ+. ((↓ratreal(x) ≤ ratreal(y)) ∨ (↓ratreal(y) ≤ ratreal(x)))
Proof
Definitions occuring in Statement :
ratreal: ratreal(r),
rleq: x ≤ y,
nat_plus: ℕ+,
all: ∀x:A. B[x],
squash: ↓T,
or: P ∨ Q,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
le_int: i ≤z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
btrue: tt,
it: ⋅,
bfalse: ff,
rat-rleq-cases,
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 :
rat-rleq-cases,
lifting-strict-less,
istype-void,
strict4-decide
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:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}. ((\mdownarrow{}ratreal(x) \mleq{} ratreal(y)) \mvee{} (\mdownarrow{}ratreal(y) \mleq{} ratreal(x)))
Date html generated:
2019_10_30-AM-09_28_32
Last ObjectModification:
2019_01_11-AM-11_46_59
Theory : reals
Home
Index