Nuprl Lemma : eqmod_equiv_rel

n:ℤEquivRel(ℤ;x,y.x ≡ mod n)


Proof




Definitions occuring in Statement :  eqmod: a ≡ mod m equiv_rel: EquivRel(T;x,y.E[x; y]) all: x:A. B[x] int:
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: c∧ B sym: Sym(T;x,y.E[x; y]) implies:  Q guard: {T} uall: [x:A]. B[x] prop: trans: Trans(T;x,y.E[x; y]) uimplies: 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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