Nuprl Lemma : nc-1-lemma
∀J:fset(ℕ). ∀j:ℕ. ∀i:{i:names(J)| ¬i ∈ J} . (((j1) i) = <i> ∈ Point(dM(J)))
Proof
Definitions occuring in Statement :
nc-1: (i1),
dM_inc: <x>,
dM: dM(I),
names: names(I),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
all: ∀x:A. B[x],
not: ¬A,
set: {x:A| B[x]} ,
apply: f a,
equal: s = t ∈ T,
lattice-point: Point(l)
Definitions unfolded in proof :
all: ∀x:A. B[x],
nc-1: (i1),
member: t ∈ T,
uall: ∀[x:A]. B[x],
names: names(I),
nat: ℕ,
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],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
prop: ℙ
Lemmas referenced :
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
dM_inc_wf,
names_wf,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
istype-int,
strong-subtype-self,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
istype-void,
istype-nat,
fset_wf,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
setIsType,
universeIsType,
functionIsType,
applyEquality,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
dependent_set_memberEquality_alt,
approximateComputation,
int_eqEquality,
Error :memTop,
independent_pairFormation
Latex:
\mforall{}J:fset(\mBbbN{}). \mforall{}j:\mBbbN{}. \mforall{}i:\{i:names(J)| \mneg{}i \mmember{} J\} . (((j1) i) = <i>)
Date html generated:
2020_05_20-PM-01_36_16
Last ObjectModification:
2020_01_04-PM-00_25_07
Theory : cubical!type!theory
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