Nuprl Lemma : div_nrel_wf
∀[a:ℕ]. ∀[n:ℕ+]. ∀[q:ℕ]. (Div(a;n;q) ∈ ℙ)
Proof
Definitions occuring in Statement :
div_nrel: Div(a;n;q),
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
div_nrel: Div(a;n;q),
nat_plus: ℕ+,
nat: ℕ
Lemmas referenced :
lelt_wf,
nat_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
multiplyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
addEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType
Latex:
\mforall{}[a:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[q:\mBbbN{}]. (Div(a;n;q) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-01_14_15
Last ObjectModification:
2018_09_26-PM-02_32_21
Theory : int_2
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