Nuprl Lemma : lt_transitivity_1
∀[i,j,k:ℤ]. (i < k) supposing ((j ≤ k) and i < j)
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
less_than_transitivity1,
le_wf,
member-less_than,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[i,j,k:\mBbbZ{}]. (i < k) supposing ((j \mleq{} k) and i < j)
Date html generated:
2016_05_13-PM-03_30_43
Last ObjectModification:
2015_12_26-AM-09_46_33
Theory : arithmetic
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