Nuprl Lemma : nsub_finite'
∀n:ℕ. finite'(ℕn)
Proof
Definitions occuring in Statement :
finite': finite'(T),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
finite': finite'(T),
surject: Surj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
less_than: a < b,
squash: ↓T,
inject: Inj(A;B;f),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable__exists_int_seg,
equal_wf,
int_seg_wf,
decidable__equal_int_seg,
injection_le,
subtract_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
inject_wf,
nat_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__lt,
less_than_wf,
set_subtype_base,
lelt_wf,
int_subtype_base,
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,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
uiff_transitivity,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
isectElimination,
Error :lambdaEquality_alt,
applyEquality,
hypothesisEquality,
Error :inhabitedIsType,
independent_functionElimination,
unionElimination,
Error :dependent_set_memberEquality_alt,
productElimination,
independent_isectElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType,
Error :functionIsType,
equalityTransitivity,
equalitySymmetry,
Error :productIsType,
Error :equalityIsType4,
intEquality,
applyLambdaEquality,
imageElimination,
equalityElimination,
Error :equalityIsType1,
promote_hyp,
cumulativity,
baseClosed,
baseApply,
closedConclusion
Latex:
\mforall{}n:\mBbbN{}. finite'(\mBbbN{}n)
Date html generated:
2019_06_20-PM-02_18_46
Last ObjectModification:
2018_10_06-AM-11_24_02
Theory : equipollence!!cardinality!
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