Nuprl Lemma : dM-deq_wf
∀[I:fset(ℕ)]. (dM-deq(I) ∈ EqDecider(Point(dM(I))))
Proof
Definitions occuring in Statement :
dM-deq: dM-deq(I),
dM: dM(I),
lattice-point: Point(l),
fset: fset(T),
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dM-deq: dM-deq(I),
subtype_rel: A ⊆r B,
squash: ↓T,
prop: ℙ,
lattice-point: Point(l),
record-select: r.x,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
dM: dM(I),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
true: True
Lemmas referenced :
names-deq_wf,
names_wf,
free-dml-deq_wf,
DeMorgan-algebra-axioms_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure_wf,
subtype_rel_transitivity,
DeMorgan-algebra-structure-subtype,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
DeMorgan-algebra-structure_wf,
subtype_rel_set,
dM_wf,
lattice-point_wf,
true_wf,
squash_wf,
deq_wf,
nat_wf,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
applyEquality,
lambdaEquality,
hyp_replacement,
hypothesisEquality,
imageElimination,
universeEquality,
instantiate,
productEquality,
independent_isectElimination,
cumulativity,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[I:fset(\mBbbN{})]. (dM-deq(I) \mmember{} EqDecider(Point(dM(I))))
Date html generated:
2016_05_18-AM-11_56_29
Last ObjectModification:
2016_01_18-PM-01_04_51
Theory : cubical!type!theory
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