Nuprl Lemma : divides_reflexivity
∀a:ℤ. (a | a)
Proof
Definitions occuring in Statement :
divides: b | a,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
divides: b | a,
exists: ∃x:A. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
istype-int,
decidable__equal_int,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermMultiply_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :dependent_pairFormation_alt,
natural_numberEquality,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
unionElimination,
isectElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
int_eqEquality,
hypothesisEquality,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
Error :universeIsType,
Error :equalityIsType4,
Error :inhabitedIsType,
applyEquality,
multiplyEquality
Latex:
\mforall{}a:\mBbbZ{}. (a | a)
Date html generated:
2019_06_20-PM-02_20_04
Last ObjectModification:
2018_10_03-AM-00_35_41
Theory : num_thy_1
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