Nuprl Lemma : free-dl-join_wf
∀[X:Type]. ∀[as,bs:free-dl-type(X)]. (free-dl-join(as;bs) ∈ free-dl-type(X))
Proof
Definitions occuring in Statement :
free-dl-join: free-dl-join(as;bs),
free-dl-type: free-dl-type(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dl-type: free-dl-type(X),
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
cand: A c∧ B,
free-dl-join: free-dl-join(as;bs),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
equiv_rel: EquivRel(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
dlattice-eq: dlattice-eq(X;as;bs)
Lemmas referenced :
dlattice-eq-equiv,
free-dl-type_wf,
list_wf,
dlattice-eq_wf,
quotient_wf,
quotient-member-eq,
append_wf,
equal-wf-base,
equal_wf,
member_wf,
squash_wf,
true_wf,
dlattice-order-append
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality,
because_Cache,
universeEquality,
promote_hyp,
lambdaFormation,
lambdaEquality,
independent_isectElimination,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination,
pointwiseFunctionality,
pertypeElimination,
productElimination,
productEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[X:Type]. \mforall{}[as,bs:free-dl-type(X)]. (free-dl-join(as;bs) \mmember{} free-dl-type(X))
Date html generated:
2017_10_05-AM-00_31_41
Last ObjectModification:
2017_07_28-AM-09_13_20
Theory : lattices
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