Nuprl Lemma : le_functionality
∀[a,b,c,d:ℤ]. ({a ≤ d supposing b ≤ c}) supposing ((c ≤ d) and (b ≥ a ))
Proof
Definitions occuring in Statement :
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 ,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
le_transitivity,
le_wf,
less_than'_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,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
voidElimination
Latex:
\mforall{}[a,b,c,d:\mBbbZ{}]. (\{a \mleq{} d supposing b \mleq{} c\}) supposing ((c \mleq{} d) and (b \mgeq{} a ))
Date html generated:
2016_05_13-PM-03_30_49
Last ObjectModification:
2015_12_26-AM-09_46_27
Theory : arithmetic
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