Nuprl Lemma : real-interval-lattice_wf
∀[I:Interval]. (real-interval-lattice(I) ∈ DistributiveLattice)
Proof
Definitions occuring in Statement :
real-interval-lattice: real-interval-lattice(I),
distributive-lattice: DistributiveLattice,
interval: Interval,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-interval-lattice: real-interval-lattice(I),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
rmin: rmin(x;y),
squash: ↓T,
real: ℝ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_stable: SqStable(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
rmax: rmax(x;y)
Lemmas referenced :
mk-distributive-lattice_wf,
real_wf,
i-member_wf,
rmin_wf,
rmin-i-member,
rmax_wf,
rmax-i-member,
implies-equal-real,
equal_wf,
imin_com,
imin_wf,
iff_weakening_equal,
nat_plus_wf,
sq_stable__i-member,
set_wf,
imax_com,
imax_wf,
imin_assoc,
imax_assoc,
rmax-rmin-absorption-strong,
rmin-rmax-absorption-strong,
rmin-rmax-distrib-strong,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
dependent_set_memberEquality,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
independent_isectElimination,
applyEquality,
imageElimination,
intEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
productElimination,
isect_memberEquality,
axiomEquality,
independent_pairFormation
Latex:
\mforall{}[I:Interval]. (real-interval-lattice(I) \mmember{} DistributiveLattice)
Date html generated:
2017_10_05-AM-00_43_17
Last ObjectModification:
2017_07_28-AM-09_17_55
Theory : lattices
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