Nuprl Lemma : less_than_functionality
∀[a,b,c,d:ℤ]. ({a < d supposing b < c}) supposing ((c ≤ d) and (b ≥ a ))
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
ge: i ≥ j ,
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
le: A ≤ B,
and: P ∧ Q,
ge: i ≥ j ,
prop: ℙ
Lemmas referenced :
less_than_transitivity2,
less_than_transitivity1,
less_than_wf,
member-less_than,
le_wf,
ge_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,
equalityTransitivity,
equalitySymmetry,
because_Cache,
intEquality
Latex:
\mforall{}[a,b,c,d:\mBbbZ{}]. (\{a < d supposing b < c\}) supposing ((c \mleq{} d) and (b \mgeq{} a ))
Date html generated:
2016_05_13-PM-03_30_51
Last ObjectModification:
2015_12_26-AM-09_46_30
Theory : arithmetic
Home
Index