Nuprl Lemma : add_functionality_wrt_eqmod
∀m,a,a',b,b':ℤ. ((a ≡ a' mod m) ⇒ (b ≡ b' mod m) ⇒ ((a + b) ≡ (a' + b') mod m))
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
implies: P ⇒ Q,
add: n + m,
int: ℤ
Definitions unfolded in proof :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtract: n - m,
top: Top,
prop: ℙ
Lemmas referenced :
divisor_of_sum,
subtract_wf,
add-associates,
istype-void,
minus-add,
minus-one-mul,
add-swap,
general_add_assoc,
divides_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
because_Cache,
Error :universeIsType,
Error :inhabitedIsType
Latex:
\mforall{}m,a,a',b,b':\mBbbZ{}. ((a \mequiv{} a' mod m) {}\mRightarrow{} (b \mequiv{} b' mod m) {}\mRightarrow{} ((a + b) \mequiv{} (a' + b') mod m))
Date html generated:
2019_06_20-PM-02_24_27
Last ObjectModification:
2019_01_17-AM-09_52_07
Theory : num_thy_1
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