Nuprl Lemma : geo-line-eq_weakening
∀g:EuclideanPlane. ∀l,m:Line. ((l = m ∈ Line) ⇒ l ≡ m)
Proof
Definitions occuring in Statement :
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,
geo-line-sep: geo-line-sep(g;l;m),
exists: ∃x:A. B[x],
and: P ∧ Q,
geo-colinear: Colinear(a;b;c),
cand: A c∧ B,
member: t ∈ T,
oriented-plane: OrientedPlane,
guard: {T},
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
lsep-not-between,
lsep-all-sym,
geo-line-sep_wf,
geo-line-eq_wf,
equal_wf,
geo-line_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
thin,
sqequalHypSubstitution,
productElimination,
independent_functionElimination,
introduction,
extract_by_obid,
dependent_functionElimination,
sqequalRule,
hypothesisEquality,
because_Cache,
independent_pairFormation,
isectElimination,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality
Latex:
\mforall{}g:EuclideanPlane. \mforall{}l,m:Line. ((l = m) {}\mRightarrow{} l \mequiv{} m)
Date html generated:
2018_05_22-PM-01_01_39
Last ObjectModification:
2018_02_07-PM-04_25_13
Theory : euclidean!plane!geometry
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