Nuprl Lemma : assert_of_le_int
∀[x,y:ℤ]. uiff(↑x ≤z y;x ≤ y)
Proof
Definitions occuring in Statement :
le_int: i ≤z j,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
le_int: i ≤z j,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
bool: 𝔹,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
gt: i > j,
guard: {T}
Lemmas referenced :
less_than'_wf,
assert_wf,
bnot_wf,
lt_int_wf,
true_wf,
false_wf,
le_wf,
equal_wf,
bool_wf,
iff_weakening_uiff,
not_wf,
assert_of_bnot,
uiff_wf,
not-gt-2,
less_than_wf,
less_than_transitivity1,
less_than_irreflexivity,
assert_of_lt_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
because_Cache,
sqequalRule,
isect_memberFormation,
productElimination,
independent_pairEquality,
isect_memberEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
unionElimination,
independent_functionElimination,
voidElimination,
addLevel,
independent_pairFormation,
independent_isectElimination,
cumulativity,
instantiate
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(\muparrow{}x \mleq{}z y;x \mleq{} y)
Date html generated:
2018_05_21-PM-00_02_12
Last ObjectModification:
2018_05_19-AM-07_13_22
Theory : arithmetic
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