Nuprl Lemma : geo-seg-congruent_weakening
∀e:BasicGeometry. ∀[s1,s2:geo-segment(e)]. geo-seg-congruent(e; s1; s2) supposing s1 = s2 ∈ geo-segment(e)
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],
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
basic-geometry: BasicGeometry,
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-segment_wf,
equal_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-congruent_wf,
geo-seg2_wf,
geo-seg1_wf,
geo-congruent-refl
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
applyLambdaEquality,
equalitySymmetry,
hyp_replacement,
because_Cache,
setElimination,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
rename,
thin,
hypothesis,
axiomEquality,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[s1,s2:geo-segment(e)]. geo-seg-congruent(e; s1; s2) supposing s1 = s2
Date html generated:
2017_10_02-PM-04_45_03
Last ObjectModification:
2017_08_05-AM-09_09_32
Theory : euclidean!plane!geometry
Home
Index