Nuprl Lemma : add_zero_int_mod
∀[n:ℤ]. ∀[x:ℤ_n].  ((x + 0) = x ∈ ℤ_n)
Proof
Definitions occuring in Statement : 
int_mod: ℤ_n
, 
uall: ∀[x:A]. B[x]
, 
add: n + m
, 
natural_number: $n
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
int_mod: ℤ_n
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
Lemmas referenced : 
eqmod_wf, 
equal_wf, 
equal-wf-base, 
int_mod_wf, 
quotient-member-eq, 
eqmod_equiv_rel, 
add-zero
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
pointwiseFunctionalityForEquality, 
because_Cache, 
sqequalRule, 
pertypeElimination, 
productElimination, 
thin, 
equalityTransitivity, 
hypothesis, 
equalitySymmetry, 
intEquality, 
lambdaFormation, 
rename, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
dependent_functionElimination, 
independent_functionElimination, 
productEquality, 
isect_memberEquality, 
axiomEquality, 
lambdaEquality, 
independent_isectElimination, 
addEquality, 
natural_numberEquality
Latex:
\mforall{}[n:\mBbbZ{}].  \mforall{}[x:\mBbbZ{}\_n].    ((x  +  0)  =  x)
Date html generated:
2017_04_17-AM-09_47_38
Last ObjectModification:
2017_02_27-PM-05_44_31
Theory : num_thy_1
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