Nuprl Lemma : int-equal-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,
rationals: ℚ,
quotient: x,y:A//B[x; y],
cand: A c∧ B,
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 :
assert_of_eq_int,
eqtt_to_assert,
evalall-reduce,
int-valueall-type,
valueall-type-has-valueall,
qeq_wf,
bool_wf,
equal-wf-T-base,
int_subtype_base,
int_nzero_wf,
b-union_wf,
equal-wf-base,
equal_functionality_wrt_subtype_rel2,
int-subtype-rationals,
rationals_wf,
equal_wf
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,
pertypeElimination,
productEquality,
baseClosed,
callbyvalueReduce,
isintReduceTrue
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(x = y;x = y)
Date html generated:
2016_05_15-PM-10_37_07
Last ObjectModification:
2016_01_16-PM-09_37_29
Theory : rationals
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