Nuprl Lemma : less_than_transitivity
∀[x,y,z:ℤ]. (x < z) supposing (y < z and x < y)
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
squash: ↓T,
less_than: a < b,
less_than': less_than'(a;b)
Lemmas referenced :
member-less_than,
less_than_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
isect_memberEquality,
isect_memberFormation,
intEquality,
because_Cache,
isectElimination,
extract_by_obid,
baseClosed,
imageMemberEquality,
sqequalRule,
hypothesisEquality,
hypothesis,
independent_pairFormation,
thin,
productElimination,
cut,
introduction,
imageElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
Error :lessTransitive
Latex:
\mforall{}[x,y,z:\mBbbZ{}]. (x < z) supposing (y < z and x < y)
Date html generated:
2019_06_20-AM-11_22_43
Last ObjectModification:
2018_10_11-PM-03_46_40
Theory : arithmetic
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