Nuprl Lemma : respects-equality-face-lattice-point
∀[I,J:fset(ℕ)]. respects-equality(Point(face_lattice(I));Point(face_lattice(J)))
Proof
Definitions occuring in Statement :
face_lattice: face_lattice(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
face_lattice: face_lattice(I),
lattice-point: Point(l),
face-lattice: face-lattice(T;eq),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a,
names: names(I),
subtype_rel: A ⊆r B,
nat: ℕ,
respects-equality: respects-equality(S;T)
Lemmas referenced :
rec_select_update_lemma,
istype-void,
respects-equality-sets,
fset_wf,
names_wf,
assert_wf,
fset-antichain_wf,
union-deq_wf,
names-deq_wf,
fset-all_wf,
fset-contains-none_wf,
face-lattice-constraints_wf,
respects-equality-fset,
respects-equality-union,
subtype-base-respects-equality,
nat_wf,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
istype-int,
strong-subtype-self,
set_subtype_base,
istype-nat,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
isect_memberFormation_alt,
isectElimination,
unionEquality,
hypothesisEquality,
lambdaEquality_alt,
productEquality,
unionIsType,
universeIsType,
because_Cache,
independent_functionElimination,
independent_isectElimination,
setEquality,
applyEquality,
intEquality,
natural_numberEquality,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
isectIsTypeImplies
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. respects-equality(Point(face\_lattice(I));Point(face\_lattice(J)))
Date html generated:
2019_11_04-PM-05_32_39
Last ObjectModification:
2018_12_13-PM-00_37_01
Theory : cubical!type!theory
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