Nuprl Lemma : ptuple-continuous
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. type-family-continuous{i:l}(P;λX.ptuple(lbl,p.a[lbl;p];X))
Proof
Definitions occuring in Statement :
ptuple: ptuple(lbl,p.a[lbl; p];X),
list: T List,
type-family-continuous: type-family-continuous{i:l}(P;H),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
lambda: λx.A[x],
function: x:A ⟶ B[x],
union: left + right,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-family-continuous: type-family-continuous{i:l}(P;H),
sub-family: F ⊆ G,
all: ∀x:A. B[x],
isect-family: ⋂a:A. F[a],
subtype_rel: A ⊆r B,
ptuple: ptuple(lbl,p.a[lbl; p];X),
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
ext-eq: A ≡ B
Lemmas referenced :
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
tuple-type_wf,
map_wf,
nat_wf,
list_wf,
ptuple_wf,
istype-atom,
istype-nat,
istype-universe,
pi2_wf,
less_than_wf,
length_wf,
pi1_wf,
subtype_rel_transitivity,
tuple-type-continuous,
subtype_rel_self,
subtype_rel_weakening,
tuple-type-ext,
int_seg_wf,
subtype_rel_list,
top_wf,
map-length,
select-map,
select_wf,
int_seg_properties,
intformand_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_term_value_var_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
list-continuity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :lambdaFormation_alt,
Error :lambdaEquality_alt,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis,
sqequalHypSubstitution,
because_Cache,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
extract_by_obid,
dependent_functionElimination,
thin,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
Error :inhabitedIsType,
productElimination,
Error :equalityIstype,
Error :dependent_pairEquality_alt,
instantiate,
unionEquality,
cumulativity,
universeEquality,
isectEquality,
applyEquality,
Error :unionIsType,
setElimination,
rename,
Error :isectIsType,
axiomEquality,
Error :functionIsTypeImplies,
Error :functionIsType,
Error :isectIsTypeImplies,
applyLambdaEquality,
setEquality,
atomEquality,
closedConclusion,
independent_pairFormation,
int_eqEquality
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)].
type-family-continuous\{i:l\}(P;\mlambda{}X.ptuple(lbl,p.a[lbl;p];X))
Date html generated:
2019_06_20-PM-02_04_00
Last ObjectModification:
2019_02_22-PM-03_23_40
Theory : tuples
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