Nuprl Lemma : m-ptwise-cont_wf
∀[X:Type]. ∀[dx:metric(X)]. ∀[Y:Type]. ∀[dy:metric(Y)]. ∀[f:X ⟶ Y]. (PtwiseCONT(f:X ⟶ Y) ∈ ℙ)
Proof
Definitions occuring in Statement :
m-ptwise-cont: PtwiseCONT(f:X ⟶ Y),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
m-ptwise-cont: PtwiseCONT(f:X ⟶ Y),
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
rless: x < y,
sq_exists: ∃x:A [B[x]],
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:Type]. \mforall{}[dx:metric(X)]. \mforall{}[Y:Type]. \mforall{}[dy:metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. (PtwiseCONT(f:X {}\mrightarrow{} Y) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-11_48_27
Last ObjectModification:
2019_11_08-AM-10_03_32
Theory : reals
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