Nuprl Lemma : subinterval-subtype
∀[I,J:Interval]. {x:ℝ| x ∈ I} ⊆r {x:ℝ| x ∈ J} supposing I ⊆ J
Proof
Definitions occuring in Statement :
subinterval: I ⊆ J ,
i-member: r ∈ I,
interval: Interval,
real: ℝ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
subinterval: I ⊆ J ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Latex:
\mforall{}[I,J:Interval]. \{x:\mBbbR{}| x \mmember{} I\} \msubseteq{}r \{x:\mBbbR{}| x \mmember{} J\} supposing I \msubseteq{} J
Date html generated:
2020_05_20-AM-11_35_01
Last ObjectModification:
2020_01_08-AM-00_37_25
Theory : reals
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