Nuprl Lemma : tuple-type-ext
∀[L,L':Type List]. tuple-type(L) ≡ tuple-type(L') supposing (||L|| = ||L'|| ∈ ℤ) ∧ (∀i:ℕ||L||. L[i] ≡ L'[i])
Proof
Definitions occuring in Statement :
tuple-type: tuple-type(L),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
ext-eq: A ≡ B,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
guard: {T}
Lemmas referenced :
subtype_rel_tuple-type,
int_seg_wf,
length_wf,
istype-int,
length_wf_nat,
set_subtype_base,
le_wf,
int_subtype_base,
ext-eq_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
list_wf,
istype-le,
istype-less_than
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
Error :lambdaFormation_alt,
sqequalRule,
dependent_functionElimination,
because_Cache,
equalitySymmetry,
Error :universeIsType,
natural_numberEquality,
instantiate,
universeEquality,
independent_pairEquality,
axiomEquality,
Error :productIsType,
Error :equalityIstype,
applyEquality,
intEquality,
Error :lambdaEquality_alt,
sqequalBase,
Error :functionIsType,
closedConclusion,
setElimination,
rename,
equalityTransitivity,
unionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :dependent_set_memberEquality_alt
Latex:
\mforall{}[L,L':Type List].
tuple-type(L) \mequiv{} tuple-type(L') supposing (||L|| = ||L'||) \mwedge{} (\mforall{}i:\mBbbN{}||L||. L[i] \mequiv{} L'[i])
Date html generated:
2019_06_20-PM-02_03_06
Last ObjectModification:
2019_02_21-PM-02_27_52
Theory : tuples
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