Nuprl Lemma : sq_stable__ex_int_seg_ap
∀n,m:ℤ. ∀f:{n..m-} ⟶ 𝔹. SqStable(∃k:{n..m-}. (↑(f k)))
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
assert: ↑b,
bool: 𝔹,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
sq_stable_from_decidable,
exists_wf,
int_seg_wf,
assert_wf,
decidable__exists_int_seg,
decidable__assert,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
independent_functionElimination,
instantiate,
dependent_functionElimination,
functionEquality,
intEquality
Latex:
\mforall{}n,m:\mBbbZ{}. \mforall{}f:\{n..m\msupminus{}\} {}\mrightarrow{} \mBbbB{}. SqStable(\mexists{}k:\{n..m\msupminus{}\}. (\muparrow{}(f k)))
Date html generated:
2016_05_14-AM-07_29_18
Last ObjectModification:
2015_12_26-PM-01_26_50
Theory : int_2
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