Nuprl Lemma : strictness-decide
∀[F,G:Top]. (case ⊥ of inl(x) => F[x] | inr(x) => G[x] ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
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,
not: ¬A,
false: False,
bfalse: ff,
top: Top
Lemmas referenced :
injection-eta,
isl_wf,
top_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
bottom_diverge,
value-type-has-value,
union-value-type,
eqff_to_assert,
assert_of_bnot,
exception-not-bottom,
has-value_wf_base,
is-exception_wf,
bottom-sqle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
hypothesis,
baseClosed,
extract_by_obid,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
isectElimination,
because_Cache,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
productElimination,
sqequalRule,
voidElimination,
decideExceptionCases,
axiomSqleEquality,
unionEquality,
baseApply,
closedConclusion,
hypothesisEquality,
sqleReflexivity,
isect_memberEquality,
voidEquality,
sqequalAxiom
Latex:
\mforall{}[F,G:Top]. (case \mbot{} of inl(x) => F[x] | inr(x) => G[x] \msim{} \mbot{})
Date html generated:
2018_05_21-PM-00_02_19
Last ObjectModification:
2018_05_19-AM-07_12_51
Theory : computation
Home
Index