Nuprl Lemma : int_pi_detach
∀i:ℤ. ℤ-Detach((i)ℤ-rng)
Proof
Definitions occuring in Statement :
int_ring: ℤ-rng,
princ_ideal: (a)r,
detach: T-Detach(A),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
princ_ideal: (a)r,
detach: T-Detach(A),
int_ring: ℤ-rng,
rng_car: |r|,
pi1: fst(t),
rng_times: *,
pi2: snd(t),
infix_ap: x f y,
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
guard: {T},
exists: ∃x:A. B[x],
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
sq_type: SQType(T),
nequal: a ≠ b ∈ T ,
int_nzero: ℤ-o,
uiff: uiff(P;Q),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable__equal_int,
decidable__int_equal,
not_wf,
exists_wf,
equal-wf-base,
int_subtype_base,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermMultiply_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
subtype_base_sq,
div_rem_sum,
nequal_wf,
add-is-int-iff,
multiply-is-int-iff,
itermAdd_wf,
int_term_value_add_lemma,
false_wf,
mul-commutes,
equal_wf,
squash_wf,
true_wf,
divide-exact,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
intEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
equalityTransitivity,
equalitySymmetry,
inlFormation,
isectElimination,
lambdaEquality,
applyEquality,
baseApply,
closedConclusion,
baseClosed,
because_Cache,
inrFormation,
dependent_pairFormation,
independent_isectElimination,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
productElimination,
promote_hyp,
instantiate,
cumulativity,
multiplyEquality,
remainderEquality,
dependent_set_memberEquality,
divideEquality,
pointwiseFunctionality,
rename,
imageElimination,
universeEquality,
equalityUniverse,
levelHypothesis,
imageMemberEquality,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}i:\mBbbZ{}. \mBbbZ{}-Detach((i)\mBbbZ{}-rng)
Date html generated:
2017_10_01-AM-08_18_44
Last ObjectModification:
2017_02_28-PM-02_03_25
Theory : rings_1
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