Nuprl Lemma : geo-eqt
∀e:BasicGeometry. ∀a,b,c:{p:Point| O_X_p} .
(((a = b ∈ {p:Point| O_X_p} ) ∧ (b = c ∈ {p:Point| O_X_p} )) ⇒ (a = c ∈ {p:Point| O_X_p} ))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-X: X,
geo-O: O,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
basic-geometry: BasicGeometry,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
set_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
equal_wf
Rules used in proof :
lambdaEquality,
dependent_set_memberEquality,
rename,
setElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
setEquality,
isectElimination,
extract_by_obid,
introduction,
productEquality,
hypothesis,
equalityTransitivity,
thin,
productElimination,
sqequalHypSubstitution,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:\{p:Point| O\_X\_p\} . (((a = b) \mwedge{} (b = c)) {}\mRightarrow{} (a = c))
Date html generated:
2017_10_02-PM-06_36_27
Last ObjectModification:
2017_08_05-PM-04_45_27
Theory : euclidean!plane!geometry
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