Nuprl Lemma : decidable__exists_int_seg
∀i,j:ℤ. ∀[F:{i..j-} ⟶ ℙ{u}]. ((∀k:{i..j-}. Dec(F[k])) ⇒ Dec(∃k:{i..j-}. F[k]))
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
has-value: (a)↓,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
value-type-has-value,
int-value-type,
int_seg_decide_wf,
int_seg_wf,
all_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
rename,
introduction,
sqequalRule,
callbyvalueReduce,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
because_Cache,
lambdaEquality,
applyEquality,
instantiate,
cumulativity,
functionEquality,
universeEquality
Latex:
\mforall{}i,j:\mBbbZ{}. \mforall{}[F:\{i..j\msupminus{}\} {}\mrightarrow{} \mBbbP{}\{u\}]. ((\mforall{}k:\{i..j\msupminus{}\}. Dec(F[k])) {}\mRightarrow{} Dec(\mexists{}k:\{i..j\msupminus{}\}. F[k]))
Date html generated:
2016_05_13-PM-03_47_46
Last ObjectModification:
2015_12_26-AM-09_57_49
Theory : call!by!value_2
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