Nuprl Lemma : divisor_of_mul
∀a,b,c:ℤ. ((a | b) ⇒ (a | (b * c)))
Proof
Definitions occuring in Statement :
divides: b | a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
multiply: 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],
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top
Lemmas referenced :
divides_wf,
equal-wf-base,
int_subtype_base,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermMultiply_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
productElimination,
dependent_pairFormation,
multiplyEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality
Latex:
\mforall{}a,b,c:\mBbbZ{}. ((a | b) {}\mRightarrow{} (a | (b * c)))
Date html generated:
2016_10_21-AM-11_07_40
Last ObjectModification:
2016_07_12-AM-06_00_24
Theory : num_thy_1
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