Nuprl Lemma : exception-sqle-is-exception
∀[u,v,t:Base]. is-exception(t) supposing exception(u; v) ≤ t
Proof
Definitions occuring in Statement :
is-exception: is-exception(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
is-exception: is-exception(t),
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
base_wf,
sqle_wf_base,
is-exception_wf,
has-value_wf_base,
exception-not-bottom,
bottom_diverge
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqleTransitivity,
divergentSqle,
sqleRule,
lemma_by_obid,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
isectElimination,
baseClosed,
because_Cache,
sqequalRule,
axiomSqleEquality,
baseApply,
closedConclusion,
hypothesisEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[u,v,t:Base]. is-exception(t) supposing exception(u; v) \mleq{} t
Date html generated:
2016_05_13-PM-03_28_38
Last ObjectModification:
2016_01_14-PM-06_41_58
Theory : arithmetic
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