Nuprl Lemma : geo-add-length-property1
∀g:EuclideanPlane. ∀s1,s2:geo-segment(g). B(X|s1||s1| + |s2|)
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-length: |s|,
geo-segment: geo-segment(e),
geo-X: X,
euclidean-plane: EuclideanPlane,
geo-between: B(abc),
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-add-length: p + q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
sq_stable: SqStable(P),
basic-geometry-: BasicGeometry-,
squash: ↓T,
euclidean-plane: EuclideanPlane,
implies: P ⇒ Q,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
geo-extend_wf,
geo-O_wf,
subtype_rel_sets,
geo-point_wf,
geo-between_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-X_wf,
geo-sep_wf,
geo-Op-sep,
sq_stable__geo-between,
geo-between-symmetry,
geo-between-inner-trans,
geo-between-exchange3,
euclidean-plane_wf,
geo-segment_wf,
geo-length_wf1
Rules used in proof :
applyEquality,
because_Cache,
lambdaEquality_alt,
instantiate,
independent_isectElimination,
dependent_set_memberEquality_alt,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityIsType1,
rename,
setElimination,
universeIsType,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
inhabitedIsType,
hypothesis,
hypothesisEquality,
sqequalRule,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlane. \mforall{}s1,s2:geo-segment(g). B(X|s1||s1| + |s2|)
Date html generated:
2019_10_29-AM-09_15_42
Last ObjectModification:
2019_10_18-PM-03_16_08
Theory : euclidean!plane!geometry
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