Nuprl Lemma : geo-seg-congruent-trivial
∀e:BasicGeometry. ∀[s:geo-segment(e)]. geo-seg-congruent(e; s; s)
Proof
Definitions occuring in Statement :
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
geo-segment: geo-segment(e),
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane
Lemmas referenced :
geo-seg-congruent_weakening,
geo-segment_wf,
basic-geometry_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
independent_isectElimination,
hypothesis,
setElimination,
rename
Latex:
\mforall{}e:BasicGeometry. \mforall{}[s:geo-segment(e)]. geo-seg-congruent(e; s; s)
Date html generated:
2018_05_22-AM-11_54_18
Last ObjectModification:
2018_04_10-PM-04_51_58
Theory : euclidean!plane!geometry
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