### Nuprl Lemma : n-tuple-decomp

`∀[n:ℕ]. (n-tuple(n) ~ if (n =z 0) then Unit if (n =z 1) then Top else Top × n-tuple(n - 1) fi )`

Proof

Definitions occuring in Statement :  n-tuple: `n-tuple(n)` nat: `ℕ` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` uall: `∀[x:A]. B[x]` top: `Top` unit: `Unit` product: `x:A × B[x]` subtract: `n - m` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  n-tuple: `n-tuple(n)` tuple-type: `tuple-type(L)` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` upto: `upto(n)` from-upto: `[n, m)` ifthenelse: `if b then t else f fi ` lt_int: `i <z j` bfalse: `ff` eq_int: `(i =z j)` subtract: `n - m` btrue: `tt` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` decidable: `Dec(P)` or: `P ∨ Q` bool: `𝔹` unit: `Unit` it: `⋅` uiff: `uiff(P;Q)` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` nat_plus: `ℕ+` nequal: `a ≠ b ∈ T ` compose: `f o g`
Lemmas referenced :  nat_properties full-omega-unsat 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 map_nil_lemma list_ind_nil_lemma 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 subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int upto_decomp2 map_cons_lemma list_ind_cons_lemma null-map null-upto le_wf map-map nat_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation sqequalAxiom unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination because_Cache promote_hyp instantiate cumulativity dependent_set_memberEquality

Latex:
\mforall{}[n:\mBbbN{}].  (n-tuple(n)  \msim{}  if  (n  =\msubz{}  0)  then  Unit  if  (n  =\msubz{}  1)  then  Top  else  Top  \mtimes{}  n-tuple(n  -  1)  fi  )

Date html generated: 2018_05_21-PM-00_52_19
Last ObjectModification: 2018_05_19-AM-06_40_12

Theory : tuples

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