### Nuprl Lemma : has-value-try

`∀[t,n,B:Base].`
`  ↓((t)↓ ∧ (t?n:v.B[v] ~ t)) ∨ (∃u:Base. ((t ~ exception(n; u)) ∧ (t?n:v.B[v] ~ B[u]) ∧ (B[u])↓)) `
`  supposing (t?n:v.B[v])↓`

Proof

Definitions occuring in Statement :  has-value: `(a)↓` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` exists: `∃x:A. B[x]` squash: `↓T` or: `P ∨ Q` and: `P ∧ Q` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` or: `P ∨ Q` and: `P ∧ Q` cand: `A c∧ B` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` squash: `↓T` guard: `{T}` exists: `∃x:A. B[x]` has-value: `(a)↓` decidable: `Dec(P)` all: `∀x:A. B[x]` rev_implies: `P `` Q` not: `¬A` iff: `P `⇐⇒` Q` false: `False` assert: `↑b` ifthenelse: `if b then t else f fi ` bnot: `¬bb` bfalse: `ff` uiff: `uiff(P;Q)` btrue: `tt` it: `⋅` unit: `Unit` bool: `𝔹` implies: `P `` Q` sq_type: `SQType(T)`
Lemmas referenced :  exists_wf base_wf has-value_wf_base decidable__atom_equal_2 assert_of_bnot iff_weakening_uiff equal-wf-base not_wf bnot_wf assert_wf iff_transitivity bool_subtype_base bool_cases_sqequal equal_wf eqff_to_assert assert_of_eq_atom2 eqtt_to_assert bool_wf eq_atom_wf2 atom2_subtype_base subtype_base_sq not-exception-has-value
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction callbyvalueTry hypothesis inlFormation independent_pairFormation extract_by_obid sqequalHypSubstitution isectElimination thin sqequalRule lambdaEquality productEquality sqequalIntensionalEquality hypothesisEquality baseApply closedConclusion baseClosed imageMemberEquality inrFormation dependent_pairFormation because_Cache imageElimination isect_memberEquality equalityTransitivity equalitySymmetry unionElimination independent_isectElimination productElimination callbyvalueAtomnEq atomn_eqReduceTrueSq dependent_functionElimination impliesFunctionality voidElimination promote_hyp equalityElimination lambdaFormation independent_functionElimination atomnEquality cumulativity instantiate atomn_eqReduceFalseSq

Latex:
\mforall{}[t,n,B:Base].
\mdownarrow{}((t)\mdownarrow{}  \mwedge{}  (t?n:v.B[v]  \msim{}  t))  \mvee{}  (\mexists{}u:Base.  ((t  \msim{}  exception(n;  u))  \mwedge{}  (t?n:v.B[v]  \msim{}  B[u])  \mwedge{}  (B[u])\mdownarrow{}))
supposing  (t?n:v.B[v])\mdownarrow{}

Date html generated: 2019_06_20-AM-11_21_48
Last ObjectModification: 2018_08_04-PM-02_10_07

Theory : call!by!value_1

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