### Nuprl Lemma : function-not-int

`∀[A:Type]. ∀[B:A ⟶ Type].  ∀[f:a:A ⟶ B[a]]. (isint(f) ~ ff) supposing ↓∃a:A. value-type(B[a])`

Proof

Definitions occuring in Statement :  value-type: `value-type(T)` bfalse: `ff` btrue: `tt` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` isint: isint def exists: `∃x:A. B[x]` squash: `↓T` function: `x:A ⟶ B[x]` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  so_lambda: `λ2x.t[x]` prop: `ℙ` guard: `{T}` implies: `P `` Q` all: `∀x:A. B[x]` sq_type: `SQType(T)` has-value: `(a)↓` so_apply: `x[s]` exists: `∃x:A. B[x]` squash: `↓T` uimplies: `b supposing a` member: `t ∈ T` uall: `∀[x:A]. B[x]` or: `P ∨ Q` top: `Top` false: `False` not: `¬A`
Lemmas referenced :  value-type_wf exists_wf squash_wf bottom_diverge value-type-has-value bool_subtype_base bool_wf subtype_base_sq bfalse_wf has-value-implies-dec-isint bottom-sqle equal_wf equal-wf-base
Rules used in proof :  universeEquality lambdaEquality because_Cache isect_memberEquality sqequalRule functionEquality axiomSqEquality independent_functionElimination equalitySymmetry equalityTransitivity dependent_functionElimination callbyvalueApply hypothesisEquality applyEquality productElimination imageElimination independent_isectElimination hypothesis cumulativity isectElimination sqequalHypSubstitution extract_by_obid instantiate thin cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution pointwiseFunctionality unionElimination baseClosed voidEquality voidElimination sqequalSqle applyInt lambdaFormation

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].    \mforall{}[f:a:A  {}\mrightarrow{}  B[a]].  (isint(f)  \msim{}  ff)  supposing  \mdownarrow{}\mexists{}a:A.  value-type(B[a])

Date html generated: 2019_06_20-AM-11_21_35
Last ObjectModification: 2018_10_16-PM-02_56_26

Theory : call!by!value_1

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