Nuprl Lemma : sq_stable__ex_int_upper_ap
∀n:ℤ. ∀f:{n...} ⟶ 𝔹. SqStable(∃m:{n...}. (↑(f m)))
Proof
Definitions occuring in Statement :
int_upper: {i...},
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],
sq_stable: SqStable(P),
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
guard: {T},
and: P ∧ Q,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mu-ge-property,
mu-ge_wf,
assert_witness,
assert_wf,
squash_wf,
exists_wf,
int_upper_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
dependent_pairEquality,
applyEquality,
independent_functionElimination,
because_Cache,
sqequalRule,
lambdaEquality,
functionEquality,
intEquality
Latex:
\mforall{}n:\mBbbZ{}. \mforall{}f:\{n...\} {}\mrightarrow{} \mBbbB{}. SqStable(\mexists{}m:\{n...\}. (\muparrow{}(f m)))
Date html generated:
2016_05_14-AM-07_28_53
Last ObjectModification:
2015_12_26-PM-01_26_59
Theory : int_2
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