Nuprl Lemma : eqmod_equiv_rel
∀n:ℤ. EquivRel(ℤ;x,y.x ≡ y mod n)
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
uimplies: b supposing a
Lemmas referenced :
eqmod_inversion,
eqmod_wf,
eqmod_transitivity,
istype-int,
eqmod_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
independent_pairFormation,
Error :inhabitedIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
independent_functionElimination,
hypothesis,
Error :universeIsType,
isectElimination,
independent_isectElimination
Latex:
\mforall{}n:\mBbbZ{}. EquivRel(\mBbbZ{};x,y.x \mequiv{} y mod n)
Date html generated:
2019_06_20-PM-02_24_24
Last ObjectModification:
2018_10_03-AM-10_23_43
Theory : num_thy_1
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