Nuprl Lemma : multiply_eqmod_zero_left
∀m,x,y:ℤ. ((x ≡ 0 mod m) ⇒ ((x * y) ≡ 0 mod m))
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
implies: P ⇒ Q,
multiply: n * m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a
Lemmas referenced :
eqmod_wf,
eqmod_weakening,
zero-mul,
multiply_functionality_wrt_eqmod
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
intEquality,
dependent_functionElimination,
independent_isectElimination,
sqequalRule,
independent_functionElimination
Latex:
\mforall{}m,x,y:\mBbbZ{}. ((x \mequiv{} 0 mod m) {}\mRightarrow{} ((x * y) \mequiv{} 0 mod m))
Date html generated:
2016_05_14-PM-04_22_29
Last ObjectModification:
2015_12_26-PM-08_18_32
Theory : num_thy_1
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