### Nuprl Lemma : mu-ge_wf2

`∀[n:ℤ]. ∀[f:{n...} ⟶ (Top + Top)].  mu-ge(f;n) ∈ {n...} supposing ∃m:{n...}. (↑isl(f m))`

Proof

Definitions occuring in Statement :  mu-ge: `mu-ge(f;n)` int_upper: `{i...}` assert: `↑b` isl: `isl(x)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` top: `Top` exists: `∃x:A. B[x]` member: `t ∈ T` apply: `f a` function: `x:A ⟶ B[x]` union: `left + right` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` exists: `∃x:A. B[x]` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` mu-ge: `mu-ge(f;n)` ifthenelse: `if b then t else f fi ` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` not: `¬A` top: `Top` and: `P ∧ Q` int_upper: `{i...}` decidable: `Dec(P)` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` isl: `isl(x)` assert: `↑b` btrue: `tt` bfalse: `ff` has-value: `(a)↓`
Lemmas referenced :  exists_wf int_upper_wf assert_wf isl_wf top_wf 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 le_wf subtract_wf decidable__le intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma nat_wf subtype_base_sq int_subtype_base int_upper_properties decidable__equal_int intformeq_wf int_formula_prop_eq_lemma true_wf false_wf equal_wf value-type-has-value itermAdd_wf int_term_value_add_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry extract_by_obid isectElimination hypothesisEquality lambdaEquality applyEquality functionExtensionality isect_memberEquality because_Cache functionEquality unionEquality intEquality lambdaFormation setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation int_eqEquality dependent_functionElimination voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination unionElimination instantiate cumulativity dependent_set_memberEquality callbyvalueReduce applyLambdaEquality

Latex:
\mforall{}[n:\mBbbZ{}].  \mforall{}[f:\{n...\}  {}\mrightarrow{}  (Top  +  Top)].    mu-ge(f;n)  \mmember{}  \{n...\}  supposing  \mexists{}m:\{n...\}.  (\muparrow{}isl(f  m))

Date html generated: 2017_04_14-AM-09_18_07
Last ObjectModification: 2017_02_27-PM-03_54_24

Theory : int_2

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