Nuprl Lemma : p2J_wf
∀[a,b:ℙ^2]. p2J(a;b) ∈ ℙ^2 supposing a ≠ b
Proof
Definitions occuring in Statement :
p2J: p2J(a;b),
proj-sep: a ≠ b,
real-proj: ℙ^n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
p2J: p2J(a;b),
real-vec: ℝ^n,
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
real-proj: ℙ^n,
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
rneq: x ≠ y,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
nat_plus: ℕ+,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
eq_int: (i =z j),
req_int_terms: t1 ≡ t2
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
rsub_wf,
rmul_wf,
lelt_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_seg_wf,
proj-sep-implies,
real-vec_wf,
false_wf,
le_wf,
exists_wf,
rneq_wf,
int-to-real_wf,
proj-sep_wf,
real-proj_wf,
decidable__equal_int,
int_subtype_base,
int_seg_properties,
nat_plus_properties,
full-omega-unsat,
intformless_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
int_seg_cases,
int_seg_subtype,
intformand_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
rless-implies-rless,
rless_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 :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
addEquality,
axiomEquality,
isect_memberEquality,
intEquality,
imageElimination,
approximateComputation,
int_eqEquality,
voidEquality,
hypothesis_subsumption,
inrFormation,
inlFormation
Latex:
\mforall{}[a,b:\mBbbP{}\^{}2]. p2J(a;b) \mmember{} \mBbbP{}\^{}2 supposing a \mneq{} b
Date html generated:
2017_10_05-AM-00_20_16
Last ObjectModification:
2017_06_20-PM-02_16_38
Theory : inner!product!spaces
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