Nuprl Lemma : fl_all-fl0
∀[I:fset(ℕ)]. ∀[i:ℕ]. ∀[x:names(I+i)]. ((∀i.(x=0)) = if (x =z i) then 0 else (x=0) fi ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
fl_all: (∀i.phi),
fl0: (x=0),
face_lattice: face_lattice(I),
add-name: I+i,
names: names(I),
lattice-0: 0,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl_all: (∀i.phi),
squash: ↓T,
names: names(I),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nequal: a ≠ b ∈ T
Lemmas referenced :
fl-all-hom_wf1,
names_wf,
add-name_wf,
nat_wf,
fset_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_subtype_base,
not-added-name
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyLambdaEquality,
setElimination,
rename,
hypothesis,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
axiomEquality,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
intEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. \mforall{}[x:names(I+i)]. ((\mforall{}i.(x=0)) = if (x =\msubz{} i) then 0 else (x=0) fi )
Date html generated:
2017_10_05-AM-01_16_01
Last ObjectModification:
2017_07_28-AM-09_32_23
Theory : cubical!type!theory
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