Nuprl Lemma : geo-add-length_functionality
∀[e:BasicGeometry]. ∀[x,y,x',y':{p:Point| O_X_p} ]. (x + y ≡ x' + y') supposing (x ≡ x' and y ≡ y')
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
basic-geometry: BasicGeometry,
geo-X: X,
geo-O: O,
geo-eq: a ≡ b,
geo-between: a_b_c,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
geo-add-length: p + q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
set_wf,
geo-eq_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
geo-point_wf,
geo-add-length_wf1,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf,
geo-extend_functionality,
geo-eq_weakening,
geo-Op-sep,
subtype_rel_sets
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
setEquality,
dependent_set_memberEquality,
rename,
setElimination,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
isectElimination,
extract_by_obid,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
lambdaFormation
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x,y,x',y':\{p:Point| O\_X\_p\} ]. (x + y \mequiv{} x' + y') supposing (x \mequiv{} x' and y \mequiv{} y')
Date html generated:
2017_10_02-PM-04_53_20
Last ObjectModification:
2017_08_05-PM-04_10_23
Theory : euclidean!plane!geometry
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