Nuprl Lemma : ap2-tuple_wf_ntuple
∀[n:ℕ]. ∀[x:Top]. ∀[f,t:n-tuple(n)]. (ap2-tuple(n;f;x;t) ∈ n-tuple(n))
Proof
Definitions occuring in Statement :
ap2-tuple: ap2-tuple(len;f;x;t),
n-tuple: n-tuple(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ 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),
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,
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
guard: {T},
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
pi2: snd(t),
nequal: a ≠ b ∈ T
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,
n-tuple_wf,
top_wf,
n-tuple-decomp,
false_wf,
le_wf,
unit_wf2,
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,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
because_Cache,
unionElimination,
equalityElimination,
productElimination,
applyEquality,
promote_hyp,
instantiate,
cumulativity,
independent_pairEquality,
productEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:Top]. \mforall{}[f,t:n-tuple(n)]. (ap2-tuple(n;f;x;t) \mmember{} n-tuple(n))
Date html generated:
2017_04_17-AM-09_29_24
Last ObjectModification:
2017_02_27-PM-05_29_43
Theory : tuples
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