Nuprl Lemma : lattice-le_transitivity
∀[l:Lattice]. ∀[a,b,c:Point(l)]. (a ≤ c) supposing (a ≤ b and b ≤ c)
Proof
Definitions occuring in Statement :
lattice-le: a ≤ b,
lattice: Lattice,
lattice-point: Point(l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
lattice-le: a ≤ b,
lattice: Lattice,
and: P ∧ Q,
guard: {T},
prop: ℙ,
squash: ↓T,
true: True
Lemmas referenced :
lattice_properties,
lattice-le_wf,
lattice-point_wf,
lattice_wf,
and_wf,
equal_wf,
lattice-meet_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
hypothesis,
setElimination,
rename,
productElimination,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
lambdaEquality,
setEquality,
imageElimination,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[l:Lattice]. \mforall{}[a,b,c:Point(l)]. (a \mleq{} c) supposing (a \mleq{} b and b \mleq{} c)
Date html generated:
2016_10_26-PM-00_51_59
Last ObjectModification:
2016_07_12-AM-08_56_13
Theory : lattices
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