Nuprl Lemma : minus_functionality_wrt_eqmod
∀m,a,a':ℤ. ((a ≡ a' mod m) ⇒ ((-a) ≡ (-a') mod m))
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
implies: P ⇒ Q,
minus: -n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
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,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
eqmod_wf,
subtract_wf,
equal_wf,
int_formula_prop_wf,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_term_value_minus_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermMultiply_wf,
itermVar_wf,
itermMinus_wf,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
minusEquality,
hypothesisEquality,
cut,
lemma_by_obid,
dependent_functionElimination,
because_Cache,
hypothesis,
unionElimination,
isectElimination,
natural_numberEquality,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
multiplyEquality
Latex:
\mforall{}m,a,a':\mBbbZ{}. ((a \mequiv{} a' mod m) {}\mRightarrow{} ((-a) \mequiv{} (-a') mod m))
Date html generated:
2016_05_14-PM-04_22_16
Last ObjectModification:
2016_01_14-PM-11_39_42
Theory : num_thy_1
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