Nuprl Lemma : eqmod-zero
∀m:ℤ. (m ≡ 0 mod m)
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
eqmod: a ≡ b mod m,
divides: b | a,
exists: ∃x:A. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
subtract_wf,
equal_wf,
int_formula_prop_wf,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
natural_numberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
hypothesis,
unionElimination,
isectElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
hypothesisEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
multiplyEquality
Latex:
\mforall{}m:\mBbbZ{}. (m \mequiv{} 0 mod m)
Date html generated:
2016_05_14-PM-04_22_04
Last ObjectModification:
2016_01_14-PM-11_39_35
Theory : num_thy_1
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