Nuprl Lemma : qv-convex-all
∀[T:Type]. ∀[S:T ⟶ (ℚ List) ⟶ ℙ]. ((∀x:T. qv-convex(p.S[x;p])) ⇒ qv-convex(p.∀x:T. S[x;p]))
Proof
Definitions occuring in Statement :
qv-convex: qv-convex(p.S[p]),
rationals: ℚ,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
qv-convex: qv-convex(p.S[p]),
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
nat: ℕ,
guard: {T}
Lemmas referenced :
qle_wf,
int-subtype-rationals,
rationals_wf,
all_wf,
equal_wf,
qv-dim_wf,
subtype_rel_list,
top_wf,
nat_wf,
list_wf,
qv-convex_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
sqequalRule,
hypothesisEquality,
cut,
lemma_by_obid,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
applyEquality,
because_Cache,
lambdaEquality,
intEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[S:T {}\mrightarrow{} (\mBbbQ{} List) {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. qv-convex(p.S[x;p])) {}\mRightarrow{} qv-convex(p.\mforall{}x:T. S[x;p]))
Date html generated:
2016_05_15-PM-11_21_29
Last ObjectModification:
2015_12_27-PM-07_32_40
Theory : rationals
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