Nuprl Lemma : not-prime-square
∀[x:ℤ]. (¬prime(x * x))
Proof
Definitions occuring in Statement :
prime: prime(a),
uall: ∀[x:A]. B[x],
not: ¬A,
multiply: n * m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
uimplies: b supposing a,
atomic: atomic(a),
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
reducible: reducible(a),
exists: ∃x:A. B[x],
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
subtype_rel: A ⊆r B,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
squash: ↓T,
true: True
Lemmas referenced :
prime_imp_atomic,
prime_wf,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
nequal_wf,
not_wf,
assoced_wf,
equal-wf-base-T,
exists_wf,
int_nzero_wf,
assoced_functionality_wrt_assoced,
multiply_functionality_wrt_assoced,
assoced_weakening,
itermMinus_wf,
int_term_value_minus_lemma,
decidable__equal_int,
intformnot_wf,
itermMultiply_wf,
int_formula_prop_not_lemma,
int_term_value_mul_lemma,
subtype_base_sq,
equal_wf,
squash_wf,
true_wf,
zero_ann_a,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
multiplyEquality,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
independent_functionElimination,
voidElimination,
because_Cache,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
intEquality,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
approximateComputation,
int_eqEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
applyEquality,
baseClosed,
productEquality,
setElimination,
rename,
baseApply,
closedConclusion,
minusEquality,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
imageElimination,
universeEquality,
inlFormation,
imageMemberEquality
Latex:
\mforall{}[x:\mBbbZ{}]. (\mneg{}prime(x * x))
Date html generated:
2019_06_20-PM-02_23_18
Last ObjectModification:
2018_09_22-PM-06_29_09
Theory : num_thy_1
Home
Index