Nuprl Lemma : real-closed-interval-lattice_wf
∀[a,b:ℝ]. real-closed-interval-lattice(a;b) ∈ GeneralBoundedDistributiveLattice supposing a ≤ b
Proof
Definitions occuring in Statement :
real-closed-interval-lattice: real-closed-interval-lattice(a;b),
rleq: x ≤ y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
general-bounded-distributive-lattice: GeneralBoundedDistributiveLattice
Definitions unfolded in proof :
squash: ↓T,
sq_stable: SqStable(P),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
equiv_rel: EquivRel(T;x,y.E[x; y]),
false: False,
not: ¬A,
stable: Stable{P},
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
so_apply: x[s1;s2],
or: P ∨ Q,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
real-closed-interval-lattice: real-closed-interval-lattice(a;b),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
guard: {T}
Latex:
\mforall{}[a,b:\mBbbR{}]. real-closed-interval-lattice(a;b) \mmember{} GeneralBoundedDistributiveLattice supposing a \mleq{} b
Date html generated:
2020_05_20-AM-11_34_08
Last ObjectModification:
2020_01_16-PM-03_28_44
Theory : reals
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