Nuprl Lemma : int_mod_2_union_int_mod_3
ℤ_2 ⋃ ℤ_3 ≡ ⇃(ℤ)
Proof
Definitions occuring in Statement :
int_mod: ℤ_n,
quotient: x,y:A//B[x; y],
b-union: A ⋃ B,
ext-eq: A ≡ B,
true: True,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
true: True,
member: t ∈ T,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
gcd: gcd(a;b),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
bfalse: ff,
btrue: tt,
ext-eq: A ≡ B,
subtype_rel: A ⊆r B,
int_mod: ℤ_n,
quotient: x,y:A//B[x; y],
eqmod: a ≡ b mod m
Lemmas referenced :
subtract_wf,
one_divs_any,
eqmod_equiv_rel,
eqmod_wf,
equal-wf-base,
quotient-member-eq,
less_than_wf,
int_mod_union_int_mod,
quotient_wf,
int_mod_wf,
b-union_wf,
ext-eq_transitivity,
true_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
intEquality,
lemma_by_obid,
hypothesis,
because_Cache,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
independent_isectElimination,
dependent_set_memberEquality,
introduction,
imageMemberEquality,
hypothesisEquality,
baseClosed,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productEquality
Latex:
\mBbbZ{}\_2 \mcup{} \mBbbZ{}\_3 \mequiv{} \00D9(\mBbbZ{})
Date html generated:
2016_05_14-PM-09_27_40
Last ObjectModification:
2016_01_14-PM-11_33_03
Theory : num_thy_1
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