Nuprl Lemma : dM-basis
∀[I:fset(ℕ)]. ∀[x:Point(dM(I))]. (x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(dM(I)))
Proof
Definitions occuring in Statement :
dM: dM(I),
names-deq: NamesDeq,
names: names(I),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dl-inc: free-dl-inc(x),
lattice-fset-join: \/(s),
lattice-fset-meet: /\(s),
lattice-point: Point(l),
fset-image: f"(s),
deq-fset: deq-fset(eq),
fset: fset(T),
union-deq: union-deq(A;B;a;b),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
dM: dM(I),
top: Top
Lemmas referenced :
free-dl-basis,
names_wf,
union-deq_wf,
names-deq_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
nat_wf,
free-dma-point
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
because_Cache,
isect_memberEquality,
axiomEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:Point(dM(I))]. (x = \mbackslash{}/(\mlambda{}s./\mbackslash{}(\mlambda{}x.free-dl-inc(x)"(s))"(x)))
Date html generated:
2016_05_18-AM-11_58_29
Last ObjectModification:
2015_12_28-PM-03_09_17
Theory : cubical!type!theory
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