Nuprl Lemma : geo-line-eq_weakening2
∀g:EuclideanPlane. ∀l,m:Line. ((l = m ∈ LINE) ⇒ l ≡ m)
Proof
Definitions occuring in Statement :
geoline: LINE,
geo-line-eq: l ≡ m,
geo-line: Line,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-line-eq: l ≡ m,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
uimplies: b supposing a,
geoline: LINE,
quotient: x,y:A//B[x; y],
false: False,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
geo-line-sep_wf,
geoline_wf,
geoline-subtype1,
geo-line_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
equalityIstype,
dependent_functionElimination,
instantiate,
independent_isectElimination,
pertypeElimination,
promote_hyp,
productElimination,
productIsType,
inhabitedIsType,
independent_functionElimination,
voidElimination
Latex:
\mforall{}g:EuclideanPlane. \mforall{}l,m:Line. ((l = m) {}\mRightarrow{} l \mequiv{} m)
Date html generated:
2019_10_16-PM-02_40_10
Last ObjectModification:
2018_12_15-PM-10_06_02
Theory : euclidean!plane!geometry
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