Nuprl Lemma : assert-fl-eq
∀[I:fset(ℕ)]. ∀[x,y:Point(face_lattice(I))]. uiff(↑(x==y);x = y ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
fl-eq: (x==y),
face_lattice: face_lattice(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
face_lattice: face_lattice(I),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
cand: A c∧ B,
uiff: uiff(P;Q),
guard: {T},
rev_uimplies: rev_uimplies(P;Q),
fl-eq: (x==y),
squash: ↓T,
deq: EqDecider(T),
eqof: eqof(d)
Lemmas referenced :
lattice-point_wf,
face-lattice_wf,
names_wf,
names-deq_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
free-dist-lattice_wf,
union-deq_wf,
fset_wf,
assert_wf,
fset-antichain_wf,
all_wf,
fset-member_wf,
deq-fset_wf,
not_wf,
subtype_rel_sets,
fl-eq_wf,
face_lattice_wf,
nat_wf,
assert_witness,
subtype_rel_functionality_wrt_iff,
fl-point,
ext-eq_weakening,
free-dl-point,
free-dml-deq_wf,
deq_wf,
free-DeMorgan-lattice_wf,
equal_functionality_wrt_subtype_rel2,
subtype_rel_weakening,
ext-eq_inversion,
safe-assert-deq
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
unionEquality,
setEquality,
functionEquality,
inlEquality,
inrEquality,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
lambdaFormation,
productElimination,
isect_memberFormation,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_functionElimination,
independent_pairFormation,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
comment,
dependent_set_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x,y:Point(face\_lattice(I))]. uiff(\muparrow{}(x==y);x = y)
Date html generated:
2017_10_05-AM-01_10_29
Last ObjectModification:
2017_07_28-AM-09_29_48
Theory : cubical!type!theory
Home
Index