Nuprl Lemma : sq_stable_geo-seg-congruent
∀e:EuclideanPlaneStructure. ∀[s1,s2:geo-segment(e)]. SqStable(geo-seg-congruent(e; s1; s2))
Proof
Definitions occuring in Statement :
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
geo-segment: geo-segment(e),
euclidean-plane-structure: EuclideanPlaneStructure,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
member: t ∈ T
Lemmas referenced :
sq_stable__geo-congruent,
geo-seg1_wf,
geo-seg2_wf,
geo-segment_wf,
euclidean-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis
Latex:
\mforall{}e:EuclideanPlaneStructure. \mforall{}[s1,s2:geo-segment(e)]. SqStable(geo-seg-congruent(e; s1; s2))
Date html generated:
2018_05_22-AM-11_54_10
Last ObjectModification:
2018_05_11-PM-06_40_47
Theory : euclidean!plane!geometry
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