Nuprl Lemma : isOdd-2n+1
∀n:ℤ. (isOdd((2 * n) + 1) ~ tt)
Proof
Definitions occuring in Statement : 
isOdd: isOdd(n)
, 
btrue: tt
, 
all: ∀x:A. B[x]
, 
multiply: n * m
, 
add: n + m
, 
natural_number: $n
, 
int: ℤ
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
rev_uimplies: rev_uimplies(P;Q)
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
exists: ∃x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
sq_type: SQType(T)
, 
guard: {T}
Lemmas referenced : 
subtype_base_sq, 
bool_wf, 
bool_subtype_base, 
eqtt_to_assert, 
isOdd_wf, 
assert-isOdd, 
int_subtype_base, 
istype-int
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :lambdaFormation_alt, 
cut, 
thin, 
instantiate, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
hypothesis, 
independent_isectElimination, 
addEquality, 
multiplyEquality, 
natural_numberEquality, 
hypothesisEquality, 
productElimination, 
dependent_functionElimination, 
independent_functionElimination, 
Error :dependent_pairFormation_alt, 
Error :equalityIstype, 
Error :inhabitedIsType, 
sqequalRule, 
baseApply, 
closedConclusion, 
baseClosed, 
applyEquality, 
sqequalBase, 
equalitySymmetry, 
equalityTransitivity
Latex:
\mforall{}n:\mBbbZ{}.  (isOdd((2  *  n)  +  1)  \msim{}  tt)
Date html generated:
2019_06_20-PM-02_24_37
Last ObjectModification:
2019_02_01-AM-11_23_05
Theory : num_thy_1
Home
Index