Nuprl Lemma : impossible-equation-by-eqmod
∀[x,z,a:ℤ]. (¬(((27 * x) + (z + z) + (3 * x * z) + z) = (1 + (999 * a)) ∈ ℤ))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
not: ¬A,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
satisfiable-full-omega-tt,
intformeq_wf,
itermAdd_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
hypothesis,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
hypothesisEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
independent_functionElimination
Latex:
\mforall{}[x,z,a:\mBbbZ{}]. (\mneg{}(((27 * x) + (z + z) + (3 * x * z) + z) = (1 + (999 * a))))
Date html generated:
2017_04_17-AM-09_43_12
Last ObjectModification:
2017_02_27-PM-05_37_45
Theory : num_thy_1
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