Nuprl Lemma : seq-append_wf
∀[T:Type]. ∀[n,k:ℕ]. ∀[s:ℕn ⟶ T]. ∀[s':ℕk ⟶ T]. (seq-append(n;s;s') ∈ ℕn + k ⟶ T)
Proof
Definitions occuring in Statement :
seq-append: seq-append(n;s;s'),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
bfalse: ff,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
nat: ℕ,
int_seg: {i..j-},
seq-append: seq-append(n;s;s'),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
istype-nat,
int_seg_wf,
int_term_value_add_lemma,
itermAdd_wf,
decidable__lt,
int_formula_prop_less_lemma,
int_term_value_subtract_lemma,
intformless_wf,
itermSubtract_wf,
subtract_wf,
less_than_wf,
assert_wf,
iff_weakening_uiff,
assert-bnot,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
istype-less_than,
istype-le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
assert_of_lt_int,
eqtt_to_assert,
lt_int_wf
Rules used in proof :
universeEquality,
isectIsTypeImplies,
functionIsType,
axiomEquality,
addEquality,
cumulativity,
instantiate,
promote_hyp,
equalityIstype,
equalitySymmetry,
equalityTransitivity,
productIsType,
universeIsType,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
natural_numberEquality,
dependent_functionElimination,
imageElimination,
independent_pairFormation,
dependent_set_memberEquality_alt,
hypothesisEquality,
applyEquality,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
lambdaFormation_alt,
inhabitedIsType,
isectElimination,
extract_by_obid,
hypothesis,
because_Cache,
rename,
thin,
setElimination,
sqequalHypSubstitution,
lambdaEquality_alt,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[n,k:\mBbbN{}]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} T]. \mforall{}[s':\mBbbN{}k {}\mrightarrow{} T]. (seq-append(n;s;s') \mmember{} \mBbbN{}n + k {}\mrightarrow{} T)
Date html generated:
2019_10_15-AM-10_25_49
Last ObjectModification:
2019_10_07-PM-00_18_48
Theory : fan-theorem
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