Nuprl Lemma : gcd_p_mul
∀a,b,y,n:ℤ. (GCD(a;b;y) ⇒ GCD(n * a;n * b;n * y))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
multiply: n * m,
int: ℤ
Definitions unfolded in proof :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
divides: b | a,
exists: ∃x:A. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
divides_wf,
gcd_p_wf,
istype-int,
divides_mul,
bezout_ident,
gcd_unique,
divides_functionality_wrt_assoced,
assoced_weakening,
multiply_functionality_wrt_assoced,
divisor_of_mul,
istype-void,
divisor_of_sum,
mul-associates,
mul-swap,
mul-distributes,
mul-commutes
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
cut,
independent_pairFormation,
hypothesis,
sqequalHypSubstitution,
productElimination,
thin,
Error :productIsType,
Error :universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
multiplyEquality,
Error :inhabitedIsType,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
addEquality,
independent_isectElimination,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}a,b,y,n:\mBbbZ{}. (GCD(a;b;y) {}\mRightarrow{} GCD(n * a;n * b;n * y))
Date html generated:
2019_06_20-PM-02_22_27
Last ObjectModification:
2018_10_03-AM-00_12_26
Theory : num_thy_1
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