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
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