Nuprl Lemma : stuck-decide
∀[a:Base]
(∀[F,H:Top]. (case a of inl(x) => F[x] | inr(x) => H[x] ~ eval x = a in ⊥)) supposing
((∀b,c:Base. (if a is inl then b else c ~ c)) and
(∀b,c:Base. (if a is inr then b else c ~ c)))
Proof
Definitions occuring in Statement :
bottom: ⊥,
callbyvalue: callbyvalue,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
isinr: isinr def,
isinl: isinl def,
all: ∀x:A. B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
all: ∀x:A. B[x],
or: P ∨ Q,
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,
isl: isl(x),
assert: ↑b,
outl: outl(x),
not: ¬A,
false: False,
bfalse: ff,
outr: outr(x),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
base_wf,
all_wf,
exception-not-bottom,
bottom_diverge,
is-exception_wf,
has-value_wf_base,
assert_of_bnot,
eqff_to_assert,
not-btrue-sqeq-bfalse,
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,
baseClosed,
promote_hyp,
voidElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
sqequalAxiom,
isect_memberEquality,
lambdaEquality,
sqequalIntensionalEquality
Latex:
\mforall{}[a:Base]
(\mforall{}[F,H:Top]. (case a of inl(x) => F[x] | inr(x) => H[x] \msim{} eval x = a in \mbot{})) supposing
((\mforall{}b,c:Base. (if a is inl then b else c \msim{} c)) and
(\mforall{}b,c:Base. (if a is inr then b else c \msim{} c)))
Date html generated:
2016_05_13-PM-03_44_56
Last ObjectModification:
2016_01_14-PM-07_06_31
Theory : computation
Home
Index