Nuprl Lemma : proj-sep_symmetry
∀n:ℕ. ∀a,b:ℙ^n. (a ≠ b ⇒ b ≠ a)
Proof
Definitions occuring in Statement :
proj-sep: a ≠ b,
real-proj: ℙ^n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
proj-sep: a ≠ b,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat: ℕ,
real-vec-sep: a ≠ b,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
subtype_rel: A ⊆r B,
real: ℝ,
nat_plus: ℕ+,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
sq_stable: SqStable(P),
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
real-vec-mul: a*X,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
rev_implies: P ⇐ Q,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
absval: |i|,
sq_type: SQType(T)
Lemmas referenced :
proj-sep_wf,
real-proj_wf,
nat_wf,
real-vec-sep-symmetry,
sq_stable__less_than,
int-to-real_wf,
real_wf,
real-vec-dist_wf,
nat_plus_properties,
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,
punit_wf,
real-vec_wf,
req_wf,
real-vec-norm_wf,
real-vec-mul_wf,
real-vec-dist-dilation,
int_seg_wf,
rmul_wf,
int_seg_properties,
intformless_wf,
int_formula_prop_less_lemma,
itermSubtract_wf,
itermMultiply_wf,
req-iff-rsub-is-0,
rabs_wf,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma,
req_functionality,
real-vec-dist_functionality,
req-vec_weakening,
req_weakening,
rless_functionality,
rleq_wf,
rless_wf,
squash_wf,
true_wf,
rabs-int,
iff_weakening_equal,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
false_wf,
absval_wf,
rless-implies-rless,
rsub_wf,
rmul_functionality,
real-vec-dist-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
independent_pairFormation,
productElimination,
thin,
promote_hyp,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
applyEquality,
lambdaEquality,
sqequalRule,
because_Cache,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
setEquality,
minusEquality,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
instantiate,
cumulativity
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b:\mBbbP{}\^{}n. (a \mneq{} b {}\mRightarrow{} b \mneq{} a)
Date html generated:
2017_10_05-AM-00_17_31
Last ObjectModification:
2017_06_18-PM-02_03_55
Theory : inner!product!spaces
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