Nuprl Lemma : not-even-succ-implies-even
∀n:ℤ. ((¬↑isEven(n + 1)) ⇒ (↑isEven(n)))
Proof
Definitions occuring in Statement :
isEven: isEven(n),
assert: ↑b,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
isEven: isEven(n),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
nat_plus: ℕ+,
less_than: a < b,
less_than': less_than'(a;b),
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
int_nzero: ℤ-o,
sq_type: SQType(T)
Lemmas referenced :
equal_wf,
int_subtype_base,
subtype_base_sq,
eq_int_wf,
assert_wf,
not_wf,
int_formula_prop_wf,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermSubtract_wf,
intformle_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
less_than_wf,
mod_bounds,
iff_weakening_equal,
add-one-mod-2,
true_wf,
squash_wf,
nequal_wf,
assert_of_eq_int,
modulus_wf,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
applyEquality,
natural_numberEquality,
productElimination,
independent_isectElimination,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
introduction,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
addEquality,
addLevel,
instantiate,
cumulativity
Latex:
\mforall{}n:\mBbbZ{}. ((\mneg{}\muparrow{}isEven(n + 1)) {}\mRightarrow{} (\muparrow{}isEven(n)))
Date html generated:
2016_05_14-PM-04_23_40
Last ObjectModification:
2016_01_14-PM-11_38_11
Theory : num_thy_1
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