Nuprl Lemma : zero_divs_only_zero
∀[a:ℤ]. a = 0 ∈ ℤ supposing 0 | a
Proof
Definitions occuring in Statement :
divides: b | a,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
divides: b | a,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
and: P ∧ Q
Lemmas referenced :
divides_wf,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
itermMultiply_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesis,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
productElimination,
dependent_functionElimination,
because_Cache,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation
Latex:
\mforall{}[a:\mBbbZ{}]. a = 0 supposing 0 | a
Date html generated:
2019_06_20-PM-02_19_55
Last ObjectModification:
2018_09_26-PM-05_45_05
Theory : num_thy_1
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