Nuprl Lemma : pgeo-leq-test
∀g:ProjectivePlane. ∀l,m,l1,m1:Line. (l ≡ l1 ⇒ m ≡ m1 ⇒ l ≡ m ⇒ l1 ≡ m1)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-leq: a ≡ b,
pgeo-line: Line,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-line_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
basic-projective-plane_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
basic-projective-plane-subtype,
projective-plane-structure_subtype,
pgeo-leq_wf,
pgeo-leq_transitivity,
pgeo-leq_inversion
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}l,m,l1,m1:Line. (l \mequiv{} l1 {}\mRightarrow{} m \mequiv{} m1 {}\mRightarrow{} l \mequiv{} m {}\mRightarrow{} l1 \mequiv{} m1)
Date html generated:
2018_05_22-PM-00_45_27
Last ObjectModification:
2017_12_05-AM-08_26_44
Theory : euclidean!plane!geometry
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