Nuprl Lemma : proj-incidence_symmetry
∀[n:ℕ]. ∀[p,v:ℙ^n]. uiff(v on p;p on v)
Proof
Definitions occuring in Statement :
proj-incidence: v on p,
real-proj: ℙ^n,
nat: ℕ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
proj-incidence: v on p,
dot-product: x⋅y,
so_lambda: λ2x.t[x],
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
so_apply: x[s],
pointwise-req: x[k] = y[k] for k ∈ [n,m],
proj-rev: proj-rev(n;p),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
req_int_terms: t1 ≡ t2
Lemmas referenced :
dot-product_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,
proj-rev_wf,
real-proj_wf,
int-to-real_wf,
proj-incidence_wf,
nat_wf,
req_witness,
rsum_functionality,
subtract_wf,
rmul_wf,
add-subtract-cancel,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
int_seg_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
rmul_comm,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
rminus_wf,
itermSubtract_wf,
itermMultiply_wf,
itermMinus_wf,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_minus_lemma,
real_term_value_const_lemma,
req_inversion,
req_transitivity
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
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,
sqequalRule,
independent_pairFormation,
applyEquality,
because_Cache,
isect_memberFormation,
productElimination,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
equalityElimination,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p,v:\mBbbP{}\^{}n]. uiff(v on p;p on v)
Date html generated:
2017_10_05-AM-00_19_42
Last ObjectModification:
2017_06_17-AM-10_08_48
Theory : inner!product!spaces
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