Nuprl Lemma : punit_wf
∀[n:ℕ]. ∀[a:ℙ^n]. (u(a) ∈ ℝ^n + 1)
Proof
Definitions occuring in Statement :
punit: u(a),
real-proj: ℙ^n,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
punit: u(a),
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,
top: Top,
and: P ∧ Q,
prop: ℙ,
real-proj: ℙ^n,
rneq: x ≠ y,
guard: {T}
Lemmas referenced :
real-vec-mul_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
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,
le_wf,
rdiv_wf,
int-to-real_wf,
real-vec-norm_wf,
proj-norm-positive,
rless_wf,
real-proj_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
because_Cache,
inrFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a:\mBbbP{}\^{}n]. (u(a) \mmember{} \mBbbR{}\^{}n + 1)
Date html generated:
2017_10_05-AM-00_17_11
Last ObjectModification:
2017_06_18-PM-02_39_16
Theory : inner!product!spaces
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