Nuprl Lemma : m-interior-point_wf
∀[X,A:Type]. ∀[d:metric(X)]. ∀[p:A]. (m-interior-point(X;d;A;p) ∈ ℙ) supposing strong-subtype(A;X)
Proof
Definitions occuring in Statement :
m-interior-point: m-interior-point(X;d;A;p),
metric: metric(X),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
m-interior-point: m-interior-point(X;d;A;p),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
so_apply: x[s]
Latex:
\mforall{}[X,A:Type]. \mforall{}[d:metric(X)]. \mforall{}[p:A]. (m-interior-point(X;d;A;p) \mmember{} \mBbbP{}) supposing strong-subtype(A;X)
Date html generated:
2020_05_20-AM-11_43_32
Last ObjectModification:
2019_11_07-AM-10_10_16
Theory : reals
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