Nuprl Lemma : ratreal_wf
∀[r:ℤ × ℕ+]. (ratreal(r) ∈ ℝ)
Proof
Definitions occuring in Statement :
ratreal: ratreal(r),
real: ℝ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ratreal: ratreal(r),
subtype_rel: A ⊆r B
Lemmas referenced :
rat-to-real_wf,
nat_plus_inc_int_nzero,
istype-int,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
spreadEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productIsType,
universeIsType
Latex:
\mforall{}[r:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}]. (ratreal(r) \mmember{} \mBbbR{})
Date html generated:
2019_10_30-AM-09_16_26
Last ObjectModification:
2019_01_10-PM-00_31_47
Theory : reals
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