Nuprl Lemma : assert_of_lt_int
∀[x,y:ℤ]. uiff(↑x <z y;x < y)
Proof
Definitions occuring in Statement :
assert: ↑b,
lt_int: i <z j,
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
false: False,
true: True,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
ifthenelse: if b then t else f fi ,
assert: ↑b,
prop: ℙ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x],
lt_int: i <z j,
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
btrue: tt,
cand: A c∧ B,
squash: ↓T,
bfalse: ff,
not: ¬A,
sq_stable: SqStable(P)
Lemmas referenced :
member-less_than,
less_than_wf,
equal_wf,
false_wf,
true_wf,
bool_wf,
lt_int_wf,
assert_wf,
top_wf,
sq_stable_from_decidable,
btrue_wf,
bfalse_wf,
decidable__assert
Rules used in proof :
intEquality,
because_Cache,
independent_isectElimination,
isect_memberEquality,
independent_pairEquality,
productElimination,
independent_functionElimination,
dependent_functionElimination,
voidElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
unionElimination,
lambdaFormation,
sqequalRule,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
lessCases,
axiomSqEquality,
voidEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
imageElimination,
promote_hyp
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(\muparrow{}x <z y;x < y)
Date html generated:
2019_06_20-AM-11_20_12
Last ObjectModification:
2018_09_02-PM-02_50_31
Theory : union
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