Nuprl Lemma : decidable__all_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],
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,
so_apply: x[s],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
not: ¬A,
false: False,
guard: {T}
Lemmas referenced :
decidable__exists_int_seg,
not_wf,
int_seg_wf,
decidable__not,
all_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
sqequalRule,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
lambdaEquality,
instantiate,
applyEquality,
hypothesis,
independent_functionElimination,
cumulativity,
functionEquality,
universeEquality,
intEquality,
unionElimination,
inrFormation,
inlFormation,
because_Cache,
productElimination,
voidElimination,
dependent_pairFormation
Latex:
\mforall{}i,j:\mBbbZ{}. \mforall{}[F:\{i..j\msupminus{}\} {}\mrightarrow{} \mBbbP{}\{u\}]. ((\mforall{}k:\{i..j\msupminus{}\}. Dec(F[k])) {}\mRightarrow{} Dec(\mforall{}k:\{i..j\msupminus{}\}. F[k]))
Date html generated:
2016_05_13-PM-03_47_49
Last ObjectModification:
2015_12_26-AM-09_57_55
Theory : call!by!value_2
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