Nuprl Lemma : p2J_functionality
∀[a1,b1,a2,b2:ℙ^2]. (p2J(a1;b1) = p2J(a2;b2)) supposing (b1 = b2 and a1 = a2 and a1 ≠ b1)
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 :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
guard: {T},
iff: P ⇐⇒ Q,
sq_stable: SqStable(P),
rev_implies: P ⇐ Q,
squash: ↓T,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
real-proj: ℙ^n,
real-vec-mul: a*X,
req-vec: req-vec(n;x;y),
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
p2J: p2J(a;b),
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,
less_than: a < b,
true: True,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2
Lemmas referenced :
sq_stable__proj-eq,
false_wf,
le_wf,
p2J_wf,
proj-sep_functionality,
proj-eq-iff,
proj-eq_wf,
proj-sep_wf,
real-proj_wf,
rmul-neq-zero,
rmul_wf,
rneq_wf,
int-to-real_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,
int_seg_wf,
rsub_wf,
lelt_wf,
itermSubtract_wf,
itermMultiply_wf,
req-iff-rsub-is-0,
req_functionality,
rsub_functionality,
rmul_functionality,
req_weakening,
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 :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
productElimination,
imageElimination,
setElimination,
rename,
imageMemberEquality,
baseClosed,
dependent_pairFormation,
addEquality,
applyEquality,
lambdaEquality,
unionElimination,
instantiate,
cumulativity,
intEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis_subsumption,
approximateComputation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[a1,b1,a2,b2:\mBbbP{}\^{}2]. (p2J(a1;b1) = p2J(a2;b2)) supposing (b1 = b2 and a1 = a2 and a1 \mneq{} b1)
Date html generated:
2017_10_05-AM-00_20_24
Last ObjectModification:
2017_06_17-AM-10_09_43
Theory : inner!product!spaces
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