### Nuprl Lemma : quicksort-int-single

`∀[n:ℤ]. (quicksort-int([n]) ~ [n])`

Proof

Definitions occuring in Statement :  quicksort-int: `quicksort-int(L)` cons: `[a / b]` nil: `[]` uall: `∀[x:A]. B[x]` int: `ℤ` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` so_lambda: `λ2x.t[x]` so_apply: `x[s]` quicksort-int: `quicksort-int(L)` quicksort: `quicksort(cmp;L)` all: `∀x:A. B[x]` top: `Top` ifthenelse: `if b then t else f fi ` bfalse: `ff` callbyvalueall: callbyvalueall has-value: `(a)↓` has-valueall: `has-valueall(a)` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` prop: `ℙ` sq_type: `SQType(T)` guard: `{T}` evalall: `evalall(t)` lt_int: `i <z j` nil: `[]` it: `⋅` eq_int: `(i =z j)` btrue: `tt` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` and: `P ∧ Q` cand: `A c∧ B`
Lemmas referenced :  permutation_wf l_member_wf sorted-by_wf and_wf permutation_weakening le_wf sorted-by-single list_ind_cons_lemma list_ind_nil_lemma quicksort-int-nil nil_wf cons_wf list-valueall-type list_wf int_formula_prop_wf int_term_value_constant_lemma int_term_value_var_lemma int_term_value_subtract_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma itermConstant_wf itermVar_wf itermSubtract_wf intformeq_wf intformnot_wf satisfiable-full-omega-tt decidable__equal_int evalall-reduce int-valueall-type valueall-type-has-valueall filter_nil_lemma filter_cons_lemma reduce_hd_cons_lemma null_cons_lemma int_subtype_base list_subtype_base set_subtype_base subtype_base_sq
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin instantiate lemma_by_obid sqequalHypSubstitution isectElimination because_Cache independent_isectElimination sqequalRule hypothesis dependent_functionElimination isect_memberEquality voidElimination voidEquality intEquality hypothesisEquality callbyvalueReduce unionElimination natural_numberEquality dependent_pairFormation lambdaEquality int_eqEquality computeAll equalityTransitivity equalitySymmetry independent_functionElimination sqleReflexivity independent_pairFormation dependent_set_memberEquality setElimination rename setEquality sqequalAxiom

Latex:
\mforall{}[n:\mBbbZ{}].  (quicksort-int([n])  \msim{}  [n])

Date html generated: 2016_05_15-PM-04_30_38
Last ObjectModification: 2016_01_16-AM-11_15_17

Theory : general

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