Nuprl Lemma : mul_nzero
∀[a,b:ℤ-o]. a * b ≠ 0
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
multiply: n * m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
false: False,
int_nzero: ℤ-o,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
int_entire_a,
int_nzero_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
equal-wf-T-base,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_isectElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
applyEquality,
baseClosed,
because_Cache,
independent_functionElimination,
multiplyEquality
Latex:
\mforall{}[a,b:\mBbbZ{}\msupminus{}\msupzero{}]. a * b \mneq{} 0
Date html generated:
2017_04_17-AM-09_45_16
Last ObjectModification:
2017_02_27-PM-05_39_54
Theory : num_thy_1
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