Nuprl Lemma : seq+_wf
∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn ⟶ T]. ∀[t:T]. (s.t ∈ ℕn + 1 ⟶ T)
Proof
Definitions occuring in Statement :
seq+: s.t,
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 :
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+: s.t,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
istype-nat,
int_seg_wf,
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,
instantiate,
Error :functionIsType,
Error :isectIsTypeImplies,
axiomEquality,
addEquality,
equalitySymmetry,
equalityTransitivity,
Error :equalityIstype,
Error :productIsType,
Error :universeIsType,
voidElimination,
Error :isect_memberEquality_alt,
int_eqEquality,
Error :dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
natural_numberEquality,
dependent_functionElimination,
imageElimination,
independent_pairFormation,
Error :dependent_set_memberEquality_alt,
hypothesisEquality,
applyEquality,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
isectElimination,
extract_by_obid,
hypothesis,
because_Cache,
rename,
thin,
setElimination,
sqequalHypSubstitution,
Error :lambdaEquality_alt,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} T]. \mforall{}[t:T]. (s.t \mmember{} \mBbbN{}n + 1 {}\mrightarrow{} T)
Date html generated:
2019_06_20-PM-02_46_44
Last ObjectModification:
2019_06_06-PM-02_24_21
Theory : fan-theorem
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