Nuprl Lemma : eq-finite-seqs_wf
∀[a,b:ℕ ⟶ ℕ]. ∀[x:ℕ]. (eq-finite-seqs(a;b;x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
eq-finite-seqs: eq-finite-seqs(a;b;x),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
bfalse: ff,
prop: ℙ,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
band: p ∧b q,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
eq-finite-seqs: eq-finite-seqs(a;b;x),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
equal_wf,
false_wf,
int_seg_subtype_nat,
nat_wf,
eq_int_wf,
eqtt_to_assert,
btrue_wf,
bool_wf,
primrec_wf
Rules used in proof :
functionEquality,
isect_memberEquality,
axiomEquality,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
because_Cache,
independent_pairFormation,
rename,
setElimination,
natural_numberEquality,
functionExtensionality,
applyEquality,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
lambdaFormation,
lambdaEquality,
hypothesisEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[x:\mBbbN{}]. (eq-finite-seqs(a;b;x) \mmember{} \mBbbB{})
Date html generated:
2017_04_20-AM-07_37_06
Last ObjectModification:
2017_04_18-AM-10_47_27
Theory : continuity
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