Nuprl Lemma : p2J_symmetry
∀[a,b:ℙ^2]. p2J(a;b) = p2J(b;a) supposing a ≠ b
Proof
Definitions occuring in Statement :
p2J: p2J(a;b),
proj-eq: a = b,
proj-sep: a ≠ b,
real-proj: ℙ^n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
proj-eq: a = b,
subtype_rel: A ⊆r B,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
exists: ∃x:A. B[x],
rneq: x ≠ y,
or: P ∨ Q,
less_than: a < b,
true: True,
req-vec: req-vec(n;x;y),
real-proj: ℙ^n,
p2J: p2J(a;b),
real-vec-mul: a*X,
int_seg: {i..j-},
decidable: Dec(P),
sq_type: SQType(T),
guard: {T},
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
real-vec: ℝ^n,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2
Lemmas referenced :
proj-sep_symmetry,
proj-eq-iff,
p2J_wf,
req_witness,
rmul_wf,
int_seg_wf,
proj-sep_wf,
false_wf,
le_wf,
real-proj_wf,
rless-int,
rless_wf,
int-to-real_wf,
rneq_wf,
req-vec_wf,
real-vec-mul_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
int_seg_subtype,
int_seg_cases,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
rsub_wf,
lelt_wf,
itermSubtract_wf,
itermMultiply_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_const_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
hypothesis,
isectElimination,
independent_isectElimination,
productElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
isect_memberFormation,
lambdaEquality,
applyEquality,
natural_numberEquality,
addEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
inlFormation,
minusEquality,
setElimination,
rename,
unionElimination,
instantiate,
cumulativity,
intEquality,
hypothesis_subsumption,
approximateComputation,
int_eqEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[a,b:\mBbbP{}\^{}2]. p2J(a;b) = p2J(b;a) supposing a \mneq{} b
Date html generated:
2017_10_05-AM-00_20_35
Last ObjectModification:
2017_06_17-AM-10_09_54
Theory : inner!product!spaces
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