### Nuprl Lemma : test-mutual-corec-ext

`test-mutual-corec() ≡ λi.if (i =z 0)`
`                         then Unit + (test-mutual-corec() 0 × ((test-mutual-corec() 1) List))`
`                         else Unit + (test-mutual-corec() 1 × ((test-mutual-corec() 0) List))`
`                         fi `

Proof

Definitions occuring in Statement :  test-mutual-corec: `test-mutual-corec()` list: `T List` k-ext: `A ≡ B` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` unit: `Unit` apply: `f a` lambda: `λx.A[x]` product: `x:A × B[x]` union: `left + right` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` uimplies: `b supposing a` lelt: `i ≤ j < k` less_than: `a < b` squash: `↓T` true: `True` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` subtype_rel: `A ⊆r B` so_apply: `x[s]` k-monotone: `k-Monotone(T.F[T])` k-subtype: `A ⊆ B` decidable: `Dec(P)` eq_int: `(i =z j)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` strong-type-continuous: `Continuous+(T.F[T])` type-continuous: `Continuous(T.F[T])` test-mutual-corec: `test-mutual-corec()`
Lemmas referenced :  mutual-corec-ext2 false_wf le_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int unit_wf2 int_seg_wf lelt_wf list_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int decidable__equal_int int_subtype_base int_seg_properties subtype_rel_union subtype_rel_product subtype_rel_list int_seg_subtype int_seg_cases full-omega-unsat intformand_wf intformless_wf itermVar_wf itermConstant_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_wf k-subtype_wf strong-continuous-union continuous-constant strong-continuous-product continuous-id strong-continuous-list subtype_rel_weakening nat_wf
Rules used in proof :  cut introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation hypothesis hypothesisEquality lambdaEquality setElimination rename because_Cache unionElimination equalityElimination productElimination independent_isectElimination unionEquality productEquality applyEquality functionExtensionality equalityTransitivity equalitySymmetry imageMemberEquality baseClosed dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination functionEquality universeEquality isect_memberFormation intEquality hypothesis_subsumption addEquality approximateComputation int_eqEquality isect_memberEquality voidEquality axiomEquality isectEquality

Latex:
test-mutual-corec()  \mequiv{}  \mlambda{}i.if  (i  =\msubz{}  0)
then  Unit  +  (test-mutual-corec()  0  \mtimes{}  ((test-mutual-corec()  1)  List))
else  Unit  +  (test-mutual-corec()  1  \mtimes{}  ((test-mutual-corec()  0)  List))
fi

Date html generated: 2018_05_21-PM-00_31_44
Last ObjectModification: 2017_10_18-PM-06_50_26

Theory : int_2

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