Nuprl Lemma : evodd-enum_wf
∀[n:ℕ]. (evodd-enum(n) ∈ b:𝔹 × (pw-evenodd() b))
Proof
Definitions occuring in Statement :
evodd-enum: evodd-enum(n),
pw-evenodd: pw-evenodd(),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
evodd-enum: evodd-enum(n),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nat: ℕ
Lemmas referenced :
primrec_wf,
bool_wf,
pw-evenodd_wf,
btrue_wf,
evodd-zero_wf,
bnot_wf,
evodd-succ_wf,
subtype_rel-equal,
equal_wf,
bnot_bnot_elim,
iff_weakening_equal,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesis,
applyEquality,
hypothesisEquality,
dependent_pairEquality,
because_Cache,
lambdaEquality,
productElimination,
independent_isectElimination,
instantiate,
imageElimination,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
setElimination,
rename,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (evodd-enum(n) \mmember{} b:\mBbbB{} \mtimes{} (pw-evenodd() b))
Date html generated:
2017_04_14-AM-07_43_23
Last ObjectModification:
2017_02_27-PM-03_14_02
Theory : co-recursion
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