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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