Nuprl Lemma : odd-or-even
∀n:ℤ. (↑(isOdd(n) ∨bisEven(n)))
Proof
Definitions occuring in Statement :
isEven: isEven(n),
isOdd: isOdd(n),
bor: p ∨bq,
assert: ↑b,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ,
isEven: isEven(n),
isOdd: isOdd(n),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
or_wf,
eq_int_wf,
assert_wf,
assert_of_eq_int,
int_formula_prop_wf,
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_or_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformor_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
int_subtype_base,
equal-wf-base,
decidable__or,
less_than_wf,
mod_bounds,
isEven_wf,
isOdd_wf,
assert_of_bor
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
introduction,
imageMemberEquality,
baseClosed,
intEquality,
baseApply,
closedConclusion,
applyEquality,
because_Cache,
independent_functionElimination,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
addLevel,
orFunctionality
Latex:
\mforall{}n:\mBbbZ{}. (\muparrow{}(isOdd(n) \mvee{}\msubb{}isEven(n)))
Date html generated:
2016_05_14-PM-04_23_53
Last ObjectModification:
2016_01_14-PM-11_37_58
Theory : num_thy_1
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