Nuprl Lemma : geo-seg-congruent_inversion
∀e:BasicGeometry. ∀[s1,s2:geo-segment(e)]. geo-seg-congruent(e; s2; s1) supposing 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),
basic-geometry: BasicGeometry,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
member: t ∈ T,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
prop: ℙ
Lemmas referenced :
geo-congruent-symmetry,
geo-seg1_wf,
geo-seg2_wf,
geo-seg-congruent_wf,
geo-segment_wf,
basic-geometry_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
isect_memberFormation_alt,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
independent_isectElimination,
universeIsType,
inhabitedIsType
Latex:
\mforall{}e:BasicGeometry
\mforall{}[s1,s2:geo-segment(e)]. geo-seg-congruent(e; s2; s1) supposing geo-seg-congruent(e; s1; s2)
Date html generated:
2019_10_16-PM-01_14_53
Last ObjectModification:
2019_08_29-PM-02_35_57
Theory : euclidean!plane!geometry
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