Nuprl Lemma : same-parity_wf
∀[n,m:ℤ]. (same-parity(n;m) ∈ 𝔹)
Proof
Definitions occuring in Statement :
same-parity: same-parity(n;m),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
same-parity: same-parity(n;m),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
isEven_wf,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-base,
int_subtype_base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
isOdd_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
intEquality,
isect_memberEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. (same-parity(n;m) \mmember{} \mBbbB{})
Date html generated:
2017_04_17-AM-09_43_24
Last ObjectModification:
2017_02_27-PM-05_37_54
Theory : num_thy_1
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