### Nuprl Lemma : mccarthy91_wf1

`∀x:ℤ. (mccarthy91(x) ∈ {m:ℤ| m = if x ≤z 101 then 91 else x - 10 fi  ∈ ℤ} )`

Proof

Definitions occuring in Statement :  mccarthy91: `mccarthy91(x)` le_int: `i ≤z j` ifthenelse: `if b then t else f fi ` all: `∀x:A. B[x]` member: `t ∈ T` set: `{x:A| B[x]} ` subtract: `n - m` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  assert: `↑b` ifthenelse: `if b then t else f fi ` bnot: `¬bb` guard: `{T}` sq_type: `SQType(T)` bfalse: `ff` or: `P ∨ Q` decidable: `Dec(P)` squash: `↓T` true: `True` less_than': `less_than'(a;b)` less_than: `a < b` uiff: `uiff(P;Q)` btrue: `tt` it: `⋅` unit: `Unit` bool: `𝔹` mccarthy91: `mccarthy91(x)` prop: `ℙ` and: `P ∧ Q` top: `Top` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` not: `¬A` uimplies: `b supposing a` ge: `i ≥ j ` false: `False` implies: `P `` Q` nat: `ℕ` member: `t ∈ T` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` has-value: `(a)↓` rev_implies: `P `` Q` iff: `P `⇐⇒` Q` subtype_rel: `A ⊆r B` subtract: `n - m` lelt: `i ≤ j < k` int_seg: `{i..j-}` le: `A ≤ B` label: `...\$L... t` so_apply: `x[s]` so_lambda: `λ2x.t[x]`
Lemmas referenced :  nat_wf decidable__le assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal equal_wf eqff_to_assert int_term_value_subtract_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma itermSubtract_wf intformeq_wf intformnot_wf decidable__equal_int top_wf assert_of_lt_int eqtt_to_assert bool_wf lt_int_wf subtract_wf le_wf less_than_wf ge_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf full-omega-unsat nat_properties int-value-type value-type-has-value iff_weakening_equal int_term_value_add_lemma itermAdd_wf true_wf squash_wf int_subtype_base int_seg_wf lelt_wf decidable__lt int_seg_cases false_wf int_seg_subtype int_seg_properties assert_of_le_int le_int_wf equal-wf-base set_wf member_wf
Rules used in proof :  cut dependent_set_memberEquality cumulativity instantiate promote_hyp imageElimination baseClosed imageMemberEquality because_Cache sqequalAxiom isect_memberFormation lessCases productElimination equalitySymmetry equalityTransitivity equalityElimination unionElimination axiomEquality independent_pairFormation sqequalRule voidEquality voidElimination isect_memberEquality dependent_functionElimination intEquality int_eqEquality lambdaEquality dependent_pairFormation independent_functionElimination approximateComputation independent_isectElimination natural_numberEquality intWeakElimination rename setElimination hypothesis hypothesisEquality thin isectElimination sqequalHypSubstitution extract_by_obid introduction lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution addEquality callbyvalueReduce universeEquality applyEquality hypothesis_subsumption closedConclusion baseApply

Latex:
\mforall{}x:\mBbbZ{}.  (mccarthy91(x)  \mmember{}  \{m:\mBbbZ{}|  m  =  if  x  \mleq{}z  101  then  91  else  x  -  10  fi  \}  )

Date html generated: 2018_05_21-PM-00_30_40
Last ObjectModification: 2017_12_27-PM-06_46_58

Theory : int_2

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