Nuprl Lemma : p2-incidence
∀[p,v:ℙ^2]. uiff(v on p;((((v 0) * (p 0)) + ((v 1) * (p 1))) - (v 2) * (p 2)) = r0)
Proof
Definitions occuring in Statement :
proj-incidence: v on p,
real-proj: ℙ^n,
rsub: x - y,
req: x = y,
rmul: a * b,
radd: a + b,
int-to-real: r(n),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
real-proj: ℙ^n,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
nat: ℕ,
proj-incidence: v on p,
subtype_rel: A ⊆r B,
proj-rev: proj-rev(n;p),
dot-product: x⋅y,
subtract: n - m,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
lt_int: i <z j,
eq_int: (i =z j),
req_int_terms: t1 ≡ t2,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rsub_wf,
radd_wf,
rmul_wf,
false_wf,
lelt_wf,
int-to-real_wf,
proj-incidence_wf,
le_wf,
dot-product_wf,
proj-rev_wf,
real-proj_wf,
req_wf,
rsum_wf,
ifthenelse_wf,
lt_int_wf,
real_wf,
rminus_wf,
int_seg_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
eq_int_wf,
assert_of_eq_int,
int_subtype_base,
neg_assert_of_eq_int,
subtract_wf,
subtract-add-cancel,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
req-implies-req,
itermSubtract_wf,
itermMultiply_wf,
itermMinus_wf,
req-iff-rsub-is-0,
req_functionality,
rsum_unroll,
req_weakening,
radd_functionality,
rsum_single,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_const_lemma,
real_term_value_add_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_minus_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
because_Cache,
hypothesis,
sqequalRule,
dependent_set_memberEquality,
natural_numberEquality,
lambdaFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
independent_functionElimination,
addEquality,
lambdaEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
voidElimination,
intEquality,
approximateComputation,
int_eqEquality,
voidEquality
Latex:
\mforall{}[p,v:\mBbbP{}\^{}2]. uiff(v on p;((((v 0) * (p 0)) + ((v 1) * (p 1))) - (v 2) * (p 2)) = r0)
Date html generated:
2017_10_05-AM-00_19_55
Last ObjectModification:
2017_06_17-AM-10_08_53
Theory : inner!product!spaces
Home
Index