Nuprl Lemma : nth-rational_wf
∀[n:ℕ]. (nth-rational(n) ∈ ℚ)
Proof
Definitions occuring in Statement :
nth-rational: nth-rational(n),
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nth-rational: nth-rational(n),
all: ∀x:A. B[x],
implies: P ⇒ Q,
equipollent: A ~ B,
exists: ∃x:A. B[x],
pi1: fst(t),
prop: ℙ
Lemmas referenced :
equipollent-nat-rationals-ext,
equipollent_wf,
nat_wf,
rationals_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
lambdaFormation,
productElimination,
applyEquality,
functionExtensionality,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (nth-rational(n) \mmember{} \mBbbQ{})
Date html generated:
2018_05_21-PM-11_49_17
Last ObjectModification:
2017_07_26-PM-06_43_16
Theory : rationals
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