Nuprl Lemma : eq_seq_wf
∀[T:Type]. ∀[eq:T ⟶ T ⟶ 𝔹]. (eq_seq(eq) ∈ (k:ℕ × (ℕk ⟶ T)) ⟶ (k:ℕ × (ℕk ⟶ T)) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
eq_seq: eq_seq(eq),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eq_seq: eq_seq(eq),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
less_than: a < b,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
primrec_wf,
btrue_wf,
int_seg_wf,
nat_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
lelt_wf,
equal_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
bfalse_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
spreadEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
applyEquality,
functionExtensionality,
cumulativity,
natural_numberEquality,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_functionElimination,
promote_hyp,
instantiate,
productEquality,
functionEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. (eq\_seq(eq) \mmember{} (k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} T)) {}\mrightarrow{} (k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} T)) {}\mrightarrow{} \mBbbB{})
Date html generated:
2018_05_21-PM-07_42_00
Last ObjectModification:
2017_07_26-PM-05_15_52
Theory : general
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