Nuprl Lemma : int-eq-in-rationals
∀[x,y:ℤ]. uiff(x = y ∈ ℚ;x = y ∈ ℤ)
Proof
Definitions occuring in Statement :
rationals: ℚ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
implies: P ⇒ Q,
qeq: qeq(r;s),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
equal_wf,
rationals_wf,
int-subtype-rationals,
equal_functionality_wrt_subtype_rel2,
assert-qeq,
valueall-type-has-valueall,
int-valueall-type,
evalall-reduce,
assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
because_Cache,
intEquality,
independent_isectElimination,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
callbyvalueReduce,
isintReduceTrue
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(x = y;x = y)
Date html generated:
2016_05_15-PM-10_39_14
Last ObjectModification:
2015_12_27-PM-07_59_21
Theory : rationals
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