Nuprl Lemma : geo-add-length-cancel-left-lt
∀[e:BasicGeometry]. ∀[x,y,z:Length]. (z + x < z + y ⇒ x < y)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-add-length: p + q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
cand: A c∧ B,
prop: ℙ,
and: P ∧ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
geo-lt: p < q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
true: True,
squash: ↓T
Lemmas referenced :
geo-length-type_wf,
geo-lt_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
exists_wf,
geo-mk-seg_wf,
geo-length_wf,
geo-add-length_wf,
geo-le_wf,
geo-sep_wf,
iff_weakening_equal,
geo-add-length-assoc,
true_wf,
squash_wf,
geo-add-length-cancel-left-le
Rules used in proof :
lambdaEquality,
independent_isectElimination,
instantiate,
rename,
setElimination,
sqequalRule,
because_Cache,
applyEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
productEquality,
hypothesis,
promote_hyp,
independent_pairFormation,
hypothesisEquality,
dependent_pairFormation,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
universeEquality,
baseClosed,
imageMemberEquality,
natural_numberEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x,y,z:Length]. (z + x < z + y {}\mRightarrow{} x < y)
Date html generated:
2017_10_02-PM-06_19_34
Last ObjectModification:
2017_08_05-PM-04_14_00
Theory : euclidean!plane!geometry
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