Nuprl Lemma : sq_stable__geo-left-1
∀g:EuclideanPlaneStructure
(BasicGeometryAxioms(g) ⇒ (∀a,b,c:Point. (a # bc ⇒ (¬Colinear(a;b;c)))) ⇒ (∀a,b,c:Point. SqStable(a leftof bc)))
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
basic-geo-axioms: BasicGeometryAxioms(g),
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
geo-left: a leftof bc,
geo-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
sq_stable: SqStable(P),
squash: ↓T,
geo-lsep: a # bc,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
false: False,
not: ¬A,
exists: ∃x:A. B[x],
geo-eq: a ≡ b,
geo-between: B(abc),
geo-sep: a # b,
basic-geo-axioms: BasicGeometryAxioms(g),
cand: A c∧ B,
geo-colinear: Colinear(a;b;c),
guard: {T}
Latex:
\mforall{}g:EuclideanPlaneStructure
(BasicGeometryAxioms(g)
{}\mRightarrow{} (\mforall{}a,b,c:Point. (a \# bc {}\mRightarrow{} (\mneg{}Colinear(a;b;c))))
{}\mRightarrow{} (\mforall{}a,b,c:Point. SqStable(a leftof bc)))
Date html generated:
2020_05_20-AM-09_44_00
Last ObjectModification:
2020_01_27-PM-02_51_12
Theory : euclidean!plane!geometry
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