Nuprl Lemma : real-vec-extend_wf
∀[k:ℕ+]. ∀[a:ℝ^k - 1]. ∀[z:ℝ]. (a++z ∈ ℝ^k)
Proof
Definitions occuring in Statement :
real-vec-extend: a++z,
real-vec: ℝ^n,
real: ℝ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
nat: ℕ,
bfalse: ff,
prop: ℙ,
lelt: i ≤ j < k,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
nat_plus: ℕ+,
int_seg: {i..j-},
real-vec-extend: a++z,
real-vec: ℝ^n,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_plus_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_plus_properties,
real-vec_wf,
real_wf,
equal_wf,
lelt_wf,
int_seg_wf,
assert_of_lt_int,
eqtt_to_assert,
bool_wf,
subtract_wf,
lt_int_wf
Rules used in proof :
voidEquality,
voidElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
approximateComputation,
isect_memberEquality,
axiomEquality,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
independent_pairFormation,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
lambdaFormation,
natural_numberEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
extract_by_obid,
sqequalRule,
functionExtensionality,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[a:\mBbbR{}\^{}k - 1]. \mforall{}[z:\mBbbR{}]. (a++z \mmember{} \mBbbR{}\^{}k)
Date html generated:
2018_07_29-AM-09_44_02
Last ObjectModification:
2018_07_02-PM-00_41_25
Theory : reals
Home
Index