Nuprl Lemma : bexists_wf
∀A:Type. ∀as:A List. ∀f:A ⟶ 𝔹. (∃bx(:A) ∈ as. f[x] ∈ 𝔹)
Proof
Definitions occuring in Statement :
bexists: bexists,
list: T List,
bool: 𝔹,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
bexists: bexists,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
bor_mon: <𝔹,∨b>,
grp_car: |g|,
pi1: fst(t),
abmonoid: AbMon,
mon: Mon
Lemmas referenced :
mon_for_wf,
bor_mon_wf,
iabmonoid_subtype_imon,
abmonoid_subtype_iabmonoid,
subtype_rel_transitivity,
abmonoid_wf,
iabmonoid_wf,
imon_wf,
bool_wf,
grp_car_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
functionEquality,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}as:A List. \mforall{}f:A {}\mrightarrow{} \mBbbB{}. (\mexists{}\msubb{}x(:A) \mmember{} as. f[x] \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-07_38_05
Last ObjectModification:
2015_12_28-PM-05_44_38
Theory : list_2
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