Nuprl Lemma : divides_wf
∀[a,b:ℤ]. (a | b ∈ ℙ)
Proof
Definitions occuring in Statement :
divides: b | a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
divides: b | a,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
exists_wf,
equal-wf-base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality,
hypothesisEquality,
applyEquality,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType
Latex:
\mforall{}[a,b:\mBbbZ{}]. (a | b \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_19_51
Last ObjectModification:
2018_09_26-PM-05_45_20
Theory : num_thy_1
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