Nuprl Lemma : decidable__eqmod
∀m,a,b:ℤ. Dec(a ≡ b mod m)
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
decidable: Dec(P),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
decidable__divides,
subtract_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
Error :inhabitedIsType
Latex:
\mforall{}m,a,b:\mBbbZ{}. Dec(a \mequiv{} b mod m)
Date html generated:
2019_06_20-PM-02_24_04
Last ObjectModification:
2018_10_03-AM-00_13_03
Theory : num_thy_1
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