Nuprl Lemma : member-less_than
∀[a,b:ℤ]. Ax ∈ a < b supposing a < b
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ
Lemmas referenced :
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
hypothesis,
independent_pairFormation,
hypothesisEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
intEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. Ax \mmember{} a < b supposing a < b
Date html generated:
2016_05_13-PM-03_20_09
Last ObjectModification:
2016_01_14-PM-04_35_00
Theory : basic_types
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