Nuprl Lemma : tuple-equiv_wf
∀[L:(X:Type × (X ⟶ X ⟶ ℙ)) List]
(tuple-equiv(L) ∈ tuple-type(map(λp.(fst(p));L)) ⟶ tuple-type(map(λp.(fst(p));L)) ⟶ ℙ)
Proof
Definitions occuring in Statement :
tuple-equiv: tuple-equiv(L),
tuple-type: tuple-type(L),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
pi1: fst(t),
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tuple-equiv: tuple-equiv(L),
let: let,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
cand: A c∧ B,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
label: ...$L... t,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
select: L[n],
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
length_wf,
select-tuple_wf,
map_wf,
istype-universe,
int_seg_subtype_nat,
istype-false,
map-length,
istype-void,
int_seg_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal_wf,
squash_wf,
true_wf,
length-map-sq,
subtype_rel_list,
top_wf,
iff_weakening_equal,
subtype_rel_self,
select-map,
tuple-type_wf,
pi1_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
instantiate,
productEquality,
universeEquality,
functionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
productElimination,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
Error :productIsType,
Error :functionIsType,
Error :universeIsType,
independent_isectElimination,
independent_pairFormation,
Error :isect_memberEquality_alt,
voidElimination,
setElimination,
rename,
imageElimination,
unionElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
intEquality,
imageMemberEquality,
baseClosed,
axiomEquality
Latex:
\mforall{}[L:(X:Type \mtimes{} (X {}\mrightarrow{} X {}\mrightarrow{} \mBbbP{})) List]
(tuple-equiv(L) \mmember{} tuple-type(map(\mlambda{}p.(fst(p));L)) {}\mrightarrow{} tuple-type(map(\mlambda{}p.(fst(p));L)) {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_16_35
Last ObjectModification:
2019_03_18-PM-04_05_25
Theory : tuples
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