Nuprl Lemma : geo-add-length-zero
∀[e:BasicGeometry]. ∀[x:Length]. (x + X = x ∈ Length)
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
geo-X: X,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
geo-add-length: p + q,
implies: P ⇒ Q,
so_apply: x[s1;s2],
uimplies: b supposing a,
guard: {T},
so_lambda: λ2x y.t[x; y],
prop: ℙ,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
quotient: x,y:A//B[x; y],
geo-length-type: Length,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x]
Lemmas referenced :
geo-length-type_wf,
equal-wf-base,
geo-between-trivial,
geo-add-length_wf1,
geo-length-equiv,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-eq_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
geo-point_wf,
quotient-member-eq,
equal_wf,
set_wf,
geo-Op-sep,
geo-sep_wf,
subtype_rel_sets,
geo-eq_transitivity,
geo-congruent_wf,
geo-extend-property,
geo-eq_inversion,
geo-congruence-identity-sym
Rules used in proof :
axiomEquality,
isect_memberEquality,
productEquality,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality,
independent_isectElimination,
instantiate,
lambdaFormation,
lambdaEquality,
rename,
setElimination,
dependent_functionElimination,
hypothesis,
applyEquality,
hypothesisEquality,
setEquality,
isectElimination,
extract_by_obid,
thin,
productElimination,
pertypeElimination,
sqequalRule,
because_Cache,
pointwiseFunctionalityForEquality,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x:Length]. (x + X = x)
Date html generated:
2017_10_02-PM-04_53_43
Last ObjectModification:
2017_08_05-PM-04_10_34
Theory : euclidean!plane!geometry
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