Nuprl Lemma : qdiv-one
∀[q:ℚ]. ((q/1) = q ∈ ℚ)
Proof
Definitions occuring in Statement :
qdiv: (r/s),
rationals: ℚ,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
qeq: qeq(r;s),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
ifthenelse: if b then t else f fi ,
btrue: tt,
eq_int: (i =z j),
bfalse: ff,
assert: ↑b,
false: False,
prop: ℙ,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q
Lemmas referenced :
rationals_wf,
qmul-qdiv-cancel,
int-subtype-rationals,
assert-qeq,
equal-wf-base,
equal_wf,
squash_wf,
true_wf,
qmul_one_qrng,
qdiv_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
applyEquality,
sqequalRule,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
voidElimination,
baseClosed,
lambdaEquality,
imageElimination,
universeEquality,
because_Cache,
imageMemberEquality,
independent_functionElimination
Latex:
\mforall{}[q:\mBbbQ{}]. ((q/1) = q)
Date html generated:
2018_05_21-PM-11_51_17
Last ObjectModification:
2017_07_26-PM-06_44_26
Theory : rationals
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