Nuprl Lemma : decide-bottom
∀[x:Top]. (case x of inl(a) => ⊥ | inr(b) => ⊥ ~ eval u = x in ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
callbyvalue: callbyvalue,
uall: ∀[x:A]. B[x],
top: Top,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
all: ∀x:A. B[x],
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
bfalse: ff,
not: ¬A,
false: False
Lemmas referenced :
exception-not-bottom,
bottom_diverge,
is-exception_wf,
has-value_wf_base,
assert_of_bnot,
eqff_to_assert,
bottom-sqle,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
top_wf,
isl_wf,
injection-eta
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
isectElimination,
because_Cache,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
productElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
sqequalAxiom
Latex:
\mforall{}[x:Top]. (case x of inl(a) => \mbot{} | inr(b) => \mbot{} \msim{} eval u = x in \mbot{})
Date html generated:
2016_05_13-PM-03_45_09
Last ObjectModification:
2016_01_14-PM-07_06_27
Theory : computation
Home
Index