### Nuprl Lemma : int_formulaco-ext

`int_formulaco() ≡ lbl:Atom × if lbl =a "less" then left:int_term() × int_term()`
`                             if lbl =a "le" then left:int_term() × int_term()`
`                             if lbl =a "eq" then left:int_term() × int_term()`
`                             if lbl =a "and" then left:int_formulaco() × int_formulaco()`
`                             if lbl =a "or" then left:int_formulaco() × int_formulaco()`
`                             if lbl =a "implies" then left:int_formulaco() × int_formulaco()`
`                             if lbl =a "not" then int_formulaco()`
`                             else Void`
`                             fi `

Proof

Definitions occuring in Statement :  int_formulaco: `int_formulaco()` int_term: `int_term()` ifthenelse: `if b then t else f fi ` eq_atom: `x =a y` ext-eq: `A ≡ B` product: `x:A × B[x]` token: `"\$token"` atom: `Atom` void: `Void`
Definitions unfolded in proof :  int_formulaco: `int_formulaco()` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` member: `t ∈ T` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` so_apply: `x[s]` continuous-monotone: `ContinuousMonotone(T.F[T])` type-monotone: `Monotone(T.F[T])` subtype_rel: `A ⊆r B` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` strong-type-continuous: `Continuous+(T.F[T])` type-continuous: `Continuous(T.F[T])`
Lemmas referenced :  corec-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom int_term_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_atom subtype_rel_product subtype_rel_self subtype_rel_wf strong-continuous-depproduct continuous-constant strong-continuous-product continuous-id subtype_rel_weakening nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin sqequalRule lambdaEquality productEquality atomEquality hypothesisEquality tokenEquality hypothesis lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination because_Cache equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination voidEquality universeEquality independent_pairFormation isect_memberFormation axiomEquality isect_memberEquality isectEquality applyEquality functionExtensionality functionEquality

Latex:
int\_formulaco()  \mequiv{}  lbl:Atom  \mtimes{}  if  lbl  =a  "less"  then  left:int\_term()  \mtimes{}  int\_term()
if  lbl  =a  "le"  then  left:int\_term()  \mtimes{}  int\_term()
if  lbl  =a  "eq"  then  left:int\_term()  \mtimes{}  int\_term()
if  lbl  =a  "and"  then  left:int\_formulaco()  \mtimes{}  int\_formulaco()
if  lbl  =a  "or"  then  left:int\_formulaco()  \mtimes{}  int\_formulaco()
if  lbl  =a  "implies"  then  left:int\_formulaco()  \mtimes{}  int\_formulaco()
if  lbl  =a  "not"  then  int\_formulaco()
else  Void
fi

Date html generated: 2017_04_14-AM-08_59_45
Last ObjectModification: 2017_02_27-PM-03_43_05

Theory : omega

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