Nuprl Lemma : left_mul_subtract_distrib
∀[a,b,c:ℤ]. ((c * (a - b)) = ((c * a) - c * b) ∈ ℤ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
multiply: n * m,
subtract: n - m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
int_formula_prop_wf,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
itermVar_wf,
itermMultiply_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
hypothesis,
unionElimination,
isectElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
hypothesisEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
axiomEquality
Latex:
\mforall{}[a,b,c:\mBbbZ{}]. ((c * (a - b)) = ((c * a) - c * b))
Date html generated:
2016_05_14-PM-04_27_43
Last ObjectModification:
2016_01_14-PM-11_34_54
Theory : num_thy_1
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