Nuprl Lemma : sq_stable__le
∀[i,j:ℤ]. SqStable(i ≤ j)
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
le: A ≤ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
and: P ∧ Q,
not: ¬A,
false: False
Lemmas referenced :
sq_stable__and,
not_wf,
less_than'_wf,
and_wf,
member_wf,
sq_stable__not,
sq_stable__equal,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
intEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality,
voidElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. SqStable(i \mleq{} j)
Date html generated:
2016_05_13-PM-03_39_28
Last ObjectModification:
2015_12_26-AM-09_41_04
Theory : arithmetic
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