Nuprl Lemma : ap2-tuple-as-tuple
∀[n:ℕ]. ∀[f,t:n-tuple(n)]. ∀[x:Top]. (ap2-tuple(n;f;x;t) ~ tuple(n;i.f.i x t.i))
Proof
Definitions occuring in Statement :
select-tuple: x.n,
ap2-tuple: ap2-tuple(len;f;x;t),
tuple: tuple(n;i.F[i]),
n-tuple: n-tuple(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
ap2-tuple: ap2-tuple(len;f;x;t),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_type: SQType(T),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
select-tuple: x.n,
nequal: a ≠ b ∈ T ,
pi2: snd(t),
tuple: tuple(n;i.F[i]),
subtype_rel: A ⊆r B,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
nil: [],
less_than: a < b,
squash: ↓T,
int_seg: {i..j-},
pi1: fst(t),
lelt: i ≤ j < k
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
top_wf,
n-tuple_wf,
n-tuple-decomp,
false_wf,
le_wf,
tuple-decomp,
subtype_base_sq,
unit_wf2,
unit_subtype_base,
equal-unit,
it_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
upto_wf,
list_wf,
int_seg_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
map_nil_lemma,
product_subtype_list,
spread_cons_lemma,
itermAdd_wf,
int_term_value_add_lemma,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
map_cons_lemma,
int_seg_properties,
add-subtract-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
dependent_set_memberEquality,
because_Cache,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
productElimination,
promote_hyp,
applyEquality,
hypothesis_subsumption,
applyLambdaEquality,
addEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f,t:n-tuple(n)]. \mforall{}[x:Top]. (ap2-tuple(n;f;x;t) \msim{} tuple(n;i.f.i x t.i))
Date html generated:
2017_04_17-AM-09_29_47
Last ObjectModification:
2017_02_27-PM-05_31_03
Theory : tuples
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