Nuprl Lemma : p2J_on_symm
∀[a,b:ℙ^2]. p2J(a;b) on b 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],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
proj-incidence: v on p,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
subtype_rel: A ⊆r B,
real-proj: ℙ^n,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
proj-sep_symmetry,
req_witness,
dot-product_wf,
false_wf,
le_wf,
p2J_wf,
real-proj_wf,
proj-rev_wf,
int-to-real_wf,
proj-sep_wf,
proj-incidence_functionality,
p2J_symmetry,
proj-eq_weakening,
p2J_on
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
hypothesisEquality,
independent_functionElimination,
hypothesis,
sqequalRule,
isectElimination,
dependent_set_memberEquality,
addEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
independent_isectElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination
Latex:
\mforall{}[a,b:\mBbbP{}\^{}2]. p2J(a;b) on b supposing a \mneq{} b
Date html generated:
2017_10_05-AM-00_20_40
Last ObjectModification:
2017_06_17-AM-10_10_00
Theory : inner!product!spaces
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