Nuprl Lemma : code-seq1_wf
∀[k:ℕ]. ∀[s:ℕk ⟶ ℕ]. (code-seq1(k;s) ∈ ℕ)
Proof
Definitions occuring in Statement :
code-seq1: code-seq1(k;s)
,
int_seg: {i..j-}
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
function: x:A ⟶ B[x]
,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
code-seq1: code-seq1(k;s)
,
nat: ℕ
,
le: A ≤ B
,
and: P ∧ Q
,
less_than': less_than'(a;b)
,
false: False
,
not: ¬A
,
implies: P
⇒ Q
,
prop: ℙ
,
int_seg: {i..j-}
,
all: ∀x:A. B[x]
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
uiff: uiff(P;Q)
,
uimplies: b supposing a
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
Lemmas referenced :
primrec_wf,
nat_wf,
false_wf,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
int_seg_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
code-pair_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
lambdaEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
applyEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
axiomEquality,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[s:\mBbbN{}k {}\mrightarrow{} \mBbbN{}]. (code-seq1(k;s) \mmember{} \mBbbN{})
Date html generated:
2018_05_21-PM-07_55_12
Last ObjectModification:
2017_07_26-PM-05_32_48
Theory : general
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