Nuprl Lemma : p2J_on
∀[a,b:ℙ^2]. p2J(a;b) on a supposing a ≠ b
Proof
Definitions occuring in Statement :
p2J: p2J(a;b),
proj-incidence: v on p,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
p2J: p2J(a;b),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
real-proj: ℙ^n,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
true: True,
all: ∀x:A. B[x],
req_int_terms: t1 ≡ t2,
top: Top
Lemmas referenced :
p2-incidence,
p2J_wf,
proj-sep_wf,
real-proj_wf,
false_wf,
le_wf,
rsub_wf,
radd_wf,
rmul_wf,
lelt_wf,
int-to-real_wf,
itermSubtract_wf,
itermAdd_wf,
itermMultiply_wf,
itermVar_wf,
itermConstant_wf,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_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,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
sqequalRule,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
applyEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
approximateComputation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[a,b:\mBbbP{}\^{}2]. p2J(a;b) on a supposing a \mneq{} b
Date html generated:
2017_10_05-AM-00_20_29
Last ObjectModification:
2017_06_17-AM-10_09_48
Theory : inner!product!spaces
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