Nuprl Lemma : proj-incidence_functionality
∀[n:ℕ]. ∀[p1,p2,v1,v2:ℙ^n]. (uiff(v1 on p1;v2 on p2)) supposing (p1 = p2 and v1 = v2)
Proof
Definitions occuring in Statement :
proj-incidence: v on p,
proj-eq: a = b,
real-proj: ℙ^n,
nat: ℕ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
proj-incidence: v on p,
squash: ↓T,
nat: ℕ,
ge: i ≥ j ,
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
real-proj: ℙ^n,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
req-vec: req-vec(n;x;y),
proj-rev: proj-rev(n;p),
real-vec-mul: a*X,
int_seg: {i..j-},
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,
real-vec: ℝ^n,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2
Lemmas referenced :
proj-eq-iff,
sq_stable__req,
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,
int-to-real_wf,
lt_int_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,
int_seg_wf,
rmul-neq-zero,
req_witness,
real-proj_wf,
proj-incidence_wf,
proj-eq_wf,
nat_wf,
rminus_wf,
rmul_wf,
itermSubtract_wf,
itermMinus_wf,
itermMultiply_wf,
req-iff-rsub-is-0,
req_functionality,
rminus_functionality,
req_weakening,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_minus_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma,
req_wf,
real-vec-mul_wf,
uiff_transitivity,
dot-product_functionality,
dot-product-linearity2,
rmul_functionality,
rmul_preserves_req,
rmul-zero-both,
req-implies-req,
rsub_wf,
req_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
imageElimination,
isectElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
applyEquality,
because_Cache,
lambdaFormation,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity,
imageMemberEquality,
baseClosed,
independent_pairEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p1,p2,v1,v2:\mBbbP{}\^{}n]. (uiff(v1 on p1;v2 on p2)) supposing (p1 = p2 and v1 = v2)
Date html generated:
2017_10_05-AM-00_19_49
Last ObjectModification:
2017_06_17-AM-10_08_58
Theory : inner!product!spaces
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