Nuprl Lemma : destructor-product
∀[F,G:Type ⟶ Type]. (destructor{i:l}(T.F[T]) ⇒ destructor{i:l}(T.G[T]) ⇒ destructor{i:l}(T.F[T] × G[T]))
Proof
Definitions occuring in Statement :
destructor: destructor{i:l}(T.F[T]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
destructor: destructor{i:l}(T.F[T]),
all: ∀x:A. B[x],
decomp: decomp{i:l}(S.F[S];T;x),
so_apply: x[s],
so_lambda: λ2x.t[x],
ap-con: ap-con(con;L),
constructor: Constr(T.F[T]),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
sq_stable: SqStable(P),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
squash: ↓T
Lemmas referenced :
istype-universe,
subtype_rel_wf,
base_wf,
destructor_wf,
list_wf,
ap-con_wf,
firstn_wf,
length_wf,
nth_tl_wf,
append_wf,
firstn_append,
subtype_rel_list,
top_wf,
sq_stable__le,
non_neg_length,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
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,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
istype-le,
istype-less_than,
firstn_all,
nth_tl_append
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
rename,
introduction,
sqequalHypSubstitution,
isect_memberEquality_alt,
cut,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis,
inhabitedIsType,
thin,
because_Cache,
lambdaEquality_alt,
productElimination,
sqequalRule,
applyEquality,
equalityIstype,
dependent_functionElimination,
independent_functionElimination,
productIsType,
universeIsType,
setElimination,
setIsType,
instantiate,
extract_by_obid,
universeEquality,
functionIsType,
dependent_pairEquality_alt,
productEquality,
independent_pairEquality,
dependent_set_memberEquality_alt,
independent_isectElimination,
Error :memTop,
independent_pairFormation,
natural_numberEquality,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
voidElimination,
imageMemberEquality,
baseClosed,
imageElimination,
addEquality
Latex:
\mforall{}[F,G:Type {}\mrightarrow{} Type].
(destructor\{i:l\}(T.F[T]) {}\mRightarrow{} destructor\{i:l\}(T.G[T]) {}\mRightarrow{} destructor\{i:l\}(T.F[T] \mtimes{} G[T]))
Date html generated:
2020_05_20-AM-08_17_45
Last ObjectModification:
2020_01_28-AM-08_30_14
Theory : general
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