Nuprl Lemma : strictness-spread
∀[F:Top]. (let a,b = ⊥ in F[a;b] ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
false: False,
top: Top
Lemmas referenced :
bottom-sqle,
is-exception_wf,
has-value_wf_base,
exception-not-bottom,
top_wf,
product-value-type,
value-type-has-value,
bottom_diverge,
pair-eta
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueSpread,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
independent_functionElimination,
because_Cache,
independent_isectElimination,
lambdaEquality,
voidElimination,
spreadExceptionCases,
axiomSqleEquality,
productEquality,
baseClosed,
baseApply,
closedConclusion,
hypothesisEquality,
sqleReflexivity,
isect_memberEquality,
voidEquality,
sqequalAxiom
Latex:
\mforall{}[F:Top]. (let a,b = \mbot{} in F[a;b] \msim{} \mbot{})
Date html generated:
2016_05_13-PM-03_43_37
Last ObjectModification:
2016_01_14-PM-07_07_44
Theory : computation
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