Nuprl Lemma : triangle-axiom2_wf
∀g:BasicProjectivePlane. (triangle-axiom2(g) ∈ ℙ)
Proof
Definitions occuring in Statement :
triangle-axiom2: triangle-axiom2(g),
basic-projective-plane: BasicProjectivePlane,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
triangle-axiom2: triangle-axiom2(g),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
basic-projective-plane: BasicProjectivePlane,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
pgeo-point_wf,
projective-plane-structure_subtype,
basic-projective-plane-subtype,
subtype_rel_transitivity,
basic-projective-plane_wf,
projective-plane-structure_wf,
pgeo-primitives_wf,
pgeo-line_wf,
pgeo-psep_wf,
pgeo-lsep_wf,
pgeo-plsep_wf,
pgeo-incident_wf,
pgeo-meet_wf,
pgeo-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
because_Cache,
functionEquality,
dependent_functionElimination,
setElimination,
rename,
setEquality,
productEquality
Latex:
\mforall{}g:BasicProjectivePlane. (triangle-axiom2(g) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_40_36
Last ObjectModification:
2017_11_07-PM-01_57_10
Theory : euclidean!plane!geometry
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