Nuprl Lemma : strictness-isaxiom
∀[a,b:Top]. (if ⊥ = Ax then a otherwise b ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
isaxiom: if z = Ax then a otherwise b,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
not: ¬A,
implies: P ⇒ Q,
false: False,
top: Top
Lemmas referenced :
top_wf,
bottom-sqle,
is-exception_wf,
has-value_wf_base,
exception-not-bottom,
bottom_diverge
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueIsaxiom,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
independent_functionElimination,
voidElimination,
isaxiomExceptionCases,
axiomSqleEquality,
baseClosed,
isectElimination,
sqequalRule,
baseApply,
closedConclusion,
hypothesisEquality,
sqleReflexivity,
isect_memberEquality,
voidEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[a,b:Top]. (if \mbot{} = Ax then a otherwise b \msim{} \mbot{})
Date html generated:
2016_05_13-PM-03_43_46
Last ObjectModification:
2016_01_14-PM-07_07_31
Theory : computation
Home
Index