Nuprl Lemma : real-det_wf
∀[n:ℕ]. ∀[M:ℕn ⟶ ℕn ⟶ ℝ]. (|M| ∈ ℝ)
Proof
Definitions occuring in Statement :
real-det: |M|,
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-det: |M|,
let: let,
nat: ℕ,
injection: A →⟶ B,
subtype_rel: A ⊆r B,
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,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
so_apply: x[s],
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
r-list-sum_wf,
map_wf,
injection_wf,
int_seg_wf,
real_wf,
permutation-sign_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
rprod_wf,
subtract_wf,
subtract-add-cancel,
nat_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
istype-less_than,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
rminus_wf,
permutations-list_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality_alt,
hypothesisEquality,
applyEquality,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
int_eqReduceTrueSq,
dependent_set_memberEquality_alt,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
universeIsType,
productIsType,
addEquality,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
int_eqReduceFalseSq,
axiomEquality,
functionIsType,
isectIsTypeImplies
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[M:\mBbbN{}n {}\mrightarrow{} \mBbbN{}n {}\mrightarrow{} \mBbbR{}]. (|M| \mmember{} \mBbbR{})
Date html generated:
2019_10_30-AM-08_21_00
Last ObjectModification:
2019_09_18-PM-05_15_29
Theory : reals
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