Nuprl Lemma : eqmod_wf
∀[m,a,b:ℤ]. (a ≡ b mod m ∈ ℙ)
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eqmod: a ≡ b mod m
Lemmas referenced :
divides_wf,
subtract_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
intEquality,
because_Cache,
Error :universeIsType
Latex:
\mforall{}[m,a,b:\mBbbZ{}]. (a \mequiv{} b mod m \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_24_01
Last ObjectModification:
2018_09_26-PM-05_50_47
Theory : num_thy_1
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