Nuprl Lemma : divisor_of_sum
∀a,b1,b2:ℤ. ((a | b1) ⇒ (a | b2) ⇒ (a | (b1 + b2)))
Proof
Definitions occuring in Statement :
divides: b | a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
add: n + m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
divides: b | a,
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
and: P ∧ Q
Lemmas referenced :
equal_wf,
int_formula_prop_wf,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermMultiply_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
divides_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
productElimination,
dependent_pairFormation,
addEquality,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
multiplyEquality
Latex:
\mforall{}a,b1,b2:\mBbbZ{}. ((a | b1) {}\mRightarrow{} (a | b2) {}\mRightarrow{} (a | (b1 + b2)))
Date html generated:
2016_05_14-PM-04_16_18
Last ObjectModification:
2016_01_14-PM-11_42_30
Theory : num_thy_1
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