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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