Nuprl Lemma : geo-congruence-identity2
∀[e:BasicGeometry]. ∀[a,b,c,d:Point]. (a ≡ b) supposing (ab ≅ cd and c ≡ d)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-congruent: ab ≅ cd,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-eq_weakening,
geo-congruent_functionality,
geo-congruence-identity-sym,
geo-point_wf,
geo-eq_wf,
geo-congruent_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf
Rules used in proof :
productElimination,
independent_functionElimination,
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
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
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b,c,d:Point]. (a \mequiv{} b) supposing (ab \00D0 cd and c \mequiv{} d)
Date html generated:
2017_10_02-PM-04_42_56
Last ObjectModification:
2017_08_05-AM-08_42_24
Theory : euclidean!plane!geometry
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