Nuprl Lemma : pgeo-triangle-axiom1-sym
∀g:ProjectivePlane. ∀a,b,c:Point. ∀s:b ≠ a. ∀s1:a ≠ c. (c ≠ b ∨ a ⇒ b ≠ a ∨ c)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-join: p ∨ q,
pgeo-psep: a ≠ b,
pgeo-plsep: a ≠ b,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
and: P ∧ Q,
projective-plane: ProjectivePlane,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
pgeo-psep_wf,
pgeo-incident_wf,
pgeo-line_wf,
pgeo-join_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-plsep_wf,
use-triangle-axiom1
Rules used in proof :
productEquality,
because_Cache,
setEquality,
lambdaEquality,
rename,
setElimination,
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{}a,b,c:Point. \mforall{}s:b \mneq{} a. \mforall{}s1:a \mneq{} c. (c \mneq{} b \mvee{} a {}\mRightarrow{} b \mneq{} a \mvee{} c)
Date html generated:
2018_05_22-PM-00_52_29
Last ObjectModification:
2017_11_21-AM-09_52_10
Theory : euclidean!plane!geometry
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