Nuprl Lemma : seg-midpoints-equal
∀e:BasicGeometry. ∀P,Q,A,X:Point. ((P=A=X ∧ Q=A=X) ⇒ P ≡ Q)
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
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 :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-midpoint_wf,
geo-midpoint-symmetry,
symmetric-point-unicity
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
productEquality,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}P,Q,A,X:Point. ((P=A=X \mwedge{} Q=A=X) {}\mRightarrow{} P \mequiv{} Q)
Date html generated:
2017_10_02-PM-06_32_31
Last ObjectModification:
2017_08_05-PM-04_43_16
Theory : euclidean!plane!geometry
Home
Index