Nuprl Lemma : nc-1-lemma2
∀j:ℕ. ((j1) j ~ {{}})
Proof
Definitions occuring in Statement :
nc-1: (i1),
empty-fset: {},
fset-singleton: {x},
nat: ℕ,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
nc-1: (i1),
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
not: ¬A,
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,
nat_properties,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermVar_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
natural_numberEquality,
approximateComputation,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
universeIsType
Latex:
\mforall{}j:\mBbbN{}. ((j1) j \msim{} \{\{\}\})
Date html generated:
2020_05_20-PM-01_36_21
Last ObjectModification:
2020_01_04-AM-11_38_07
Theory : cubical!type!theory
Home
Index