Nuprl Lemma : decidable__equal-free-dist-lattice-with-constraints-point
∀[T:Type]
∀eq:EqDecider(T). ∀Cs:T ⟶ fset(fset(T)). ∀a,b:Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])).
Dec(a = b ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
Proof
Definitions occuring in Statement :
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
lattice-point: Point(l),
fset: fset(T),
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
free-dlwc-point,
decidable__equal_set,
fset_wf,
decidable__equal_fset,
decidable-equal-deq,
and_wf,
assert_wf,
fset-antichain_wf,
fset-all_wf,
fset-contains-none_wf,
set_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
isect_memberFormation,
lambdaFormation,
hypothesisEquality,
independent_functionElimination,
dependent_functionElimination,
lambdaEquality,
applyEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}eq:EqDecider(T). \mforall{}Cs:T {}\mrightarrow{} fset(fset(T)).
\mforall{}a,b:Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])).
Dec(a = b)
Date html generated:
2020_05_20-AM-08_48_21
Last ObjectModification:
2015_12_28-PM-01_58_54
Theory : lattices
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