Nuprl Lemma : geo-lt-add1_1
∀e:BasicGeometry. ∀p,q,r:Length. (p < q ⇒ p < q + r)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-add-length: p + q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-lt: p < q,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Lemmas referenced :
geo-le-add1,
geo-le_transitivity,
geo-add-length_wf,
geo-length_wf,
geo-mk-seg_wf,
geo-sep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-le_wf,
geo-lt_wf,
geo-length-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation_alt,
hypothesisEquality,
cut,
hypothesis,
independent_pairFormation,
introduction,
extract_by_obid,
dependent_functionElimination,
isectElimination,
because_Cache,
setElimination,
rename,
independent_isectElimination,
sqequalRule,
productIsType,
universeIsType,
applyEquality,
instantiate,
inhabitedIsType
Latex:
\mforall{}e:BasicGeometry. \mforall{}p,q,r:Length. (p < q {}\mRightarrow{} p < q + r)
Date html generated:
2019_10_16-PM-01_35_05
Last ObjectModification:
2019_01_31-PM-02_55_11
Theory : euclidean!plane!geometry
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