Nuprl Lemma : gcd_p_shift
∀a,b,y,k:ℤ. (GCD(a;b;y) ⇒ GCD(a;b + (k * a);y))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
multiply: n * m,
add: 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,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
divides_wf,
istype-int,
divisor_of_sum,
squash_wf,
true_wf,
mul_com,
subtype_rel_self,
iff_weakening_equal,
divisor_of_mul,
istype-void,
add-associates,
minus-one-mul,
mul-commutes,
mul-swap,
add-commutes,
add-mul-special,
zero-mul,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
independent_pairFormation,
Error :productIsType,
Error :universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
addEquality,
multiplyEquality,
Error :inhabitedIsType,
Error :functionIsType,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
because_Cache,
minusEquality,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}a,b,y,k:\mBbbZ{}. (GCD(a;b;y) {}\mRightarrow{} GCD(a;b + (k * a);y))
Date html generated:
2019_06_20-PM-02_21_46
Last ObjectModification:
2018_10_03-AM-00_12_07
Theory : num_thy_1
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