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: uall: [x:A]. B[x] top: Top member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: 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: le: A ≤ B less_than': less_than'(a;b) ap2-tuple: ap2-tuple(len;f;x;t) eq_int: (i =z j) subtract: m ifthenelse: if then else fi  btrue: tt decidable: Dec(P) or: P ∨ Q bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) subtype_rel: A ⊆B guard: {T} bfalse: ff sq_type: SQType(T) bnot: ¬bb assert: b pi2: snd(t) nequal: a ≠ b ∈ 
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


Home Index