Nuprl Lemma : isEven_wf
∀[n:ℤ]. (isEven(n) ∈ 𝔹)
Proof
Definitions occuring in Statement :
isEven: isEven(n),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
isEven: isEven(n),
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
eq_int_wf,
modulus_wf,
subtype_base_sq,
int_subtype_base,
equal_wf,
true_wf,
nequal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
applyEquality,
because_Cache,
axiomEquality
Latex:
\mforall{}[n:\mBbbZ{}]. (isEven(n) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-04_23_23
Last ObjectModification:
2015_12_26-PM-08_18_55
Theory : num_thy_1
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