Nuprl Lemma : punit-norm1
∀[n:ℕ]. ∀[a:ℙ^n]. (||u(a)|| = r1)
Proof
Definitions occuring in Statement :
punit: u(a),
real-proj: ℙ^n,
real-vec-norm: ||x||,
req: x = y,
int-to-real: r(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
and: P ∧ Q,
prop: ℙ,
punit: u(a),
real-proj: ℙ^n,
rneq: x ≠ y,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
rat_term_to_real: rat_term_to_real(f;t),
rtermConstant: "const",
rat_term_ind: rat_term_ind,
pi1: fst(t),
true: True,
rtermMultiply: left "*" right,
rtermDivide: num "/" denom,
rtermVar: rtermVar(var),
pi2: snd(t)
Lemmas referenced :
req_witness,
real-vec-norm_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
punit_wf,
int-to-real_wf,
real-proj_wf,
istype-nat,
real-vec-mul_wf,
rdiv_wf,
proj-norm-positive,
rless_wf,
rmul_wf,
rabs_wf,
req_functionality,
real-vec-norm-mul,
req_weakening,
real-vec-norm-nonneg,
rleq-int,
istype-false,
assert-rat-term-eq2,
rtermMultiply_wf,
rtermDivide_wf,
rtermConstant_wf,
rtermVar_wf,
rmul_functionality,
rabs-rdiv,
rneq_functionality,
rabs-of-nonneg,
rdiv_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
sqequalRule,
independent_pairFormation,
universeIsType,
voidElimination,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
inhabitedIsType,
closedConclusion,
inrFormation_alt,
productElimination,
lambdaFormation_alt
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a:\mBbbP{}\^{}n]. (||u(a)|| = r1)
Date html generated:
2020_05_20-PM-01_16_37
Last ObjectModification:
2019_12_09-PM-04_23_27
Theory : inner!product!spaces
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