Nuprl Lemma : geo-extend_functionality
∀[e:BasicGeometry]. ∀[a:Point]. ∀[b:{b:Point| a # b} ]. ∀[c,d,a':Point]. ∀[b':{b':Point| a' # b'} ]. ∀[c',d':Point].
(extend ab by cd ≡ extend a'b' by c'd') supposing (a ≡ a' and b ≡ b' and c ≡ c' and d ≡ d')
Proof
Definitions occuring in Statement :
geo-extend: extend qa by bc,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-sep: a # b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-eq: a ≡ b,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_apply: x[s],
so_lambda: λ2x.t[x]
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a:Point]. \mforall{}[b:\{b:Point| a \# b\} ]. \mforall{}[c,d,a':Point]. \mforall{}[b':\{b':Point| a' \# b'\} ].
\mforall{}[c',d':Point].
(extend ab by cd \mequiv{} extend a'b' by c'd') supposing (a \mequiv{} a' and b \mequiv{} b' and c \mequiv{} c' and d \mequiv{} d')
Date html generated:
2020_05_20-AM-09_51_36
Last ObjectModification:
2020_01_13-PM-03_24_58
Theory : euclidean!plane!geometry
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