Nuprl Lemma : r2-basic-geo-axioms
BasicGeometryAxioms(r2-eu-prim())
Proof
Definitions occuring in Statement :
r2-eu-prim: r2-eu-prim(),
basic-geo-axioms: BasicGeometryAxioms(g)
Definitions unfolded in proof :
r2-eu-prim: r2-eu-prim(),
basic-geo-axioms: BasicGeometryAxioms(g),
mk-eu-prim: mk-eu-prim,
and: P ∧ Q,
geo-ge: ab ≥ cd,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
implies: P ⇒ Q,
not: ¬A,
false: False,
guard: {T},
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
geo-sep: a # b,
rev_implies: P ⇐ Q,
rge: x ≥ y,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
or: P ∨ Q,
geo-left: a leftof bc,
geo-lsep: a # bc,
geo-between: B(abc),
real-vec-sep: a ≠ b,
sq_exists: ∃x:A [B[x]],
rless: x < y,
r2-left: r2-left(p;q;r),
geo-congruent: ab ≅ cd,
geo-length-sep: ab # cd),
rv-be: a_b_c,
cand: A c∧ B
Latex:
BasicGeometryAxioms(r2-eu-prim())
Date html generated:
2020_05_20-PM-01_10_27
Last ObjectModification:
2020_01_28-AM-10_55_10
Theory : reals!model!euclidean!geometry
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