Nuprl Lemma : stuck-spread
∀[a:Base]. ∀[F:Top]. (let x,y = a in F[x;y] ~ eval x = a in ⊥) supposing ∀b,c:Base. (if a is a pair then b otherwise c \000C~ c)
Proof
Definitions occuring in Statement :
bottom: ⊥,
callbyvalue: callbyvalue,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
ispair: if z is a pair then a otherwise b,
all: ∀x:A. B[x],
spread: spread def,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
all: ∀x:A. B[x],
pi1: fst(t),
pi2: snd(t),
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
base_wf,
all_wf,
top_wf,
exception-not-bottom,
bottom_diverge,
is-exception_wf,
has-value_wf_base,
not-btrue-sqeq-bfalse,
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,
dependent_functionElimination,
baseClosed,
promote_hyp,
independent_functionElimination,
voidElimination,
spreadExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
sqequalAxiom,
isect_memberEquality,
because_Cache,
lambdaEquality,
sqequalIntensionalEquality
Latex:
\mforall{}[a:Base]. \mforall{}[F:Top]. (let x,y = a in F[x;y] \msim{} eval x = a in \mbot{}) supposing \mforall{}b,c:Base. (if a is a pair\000C then b otherwise c \msim{} c)
Date html generated:
2016_05_13-PM-03_44_54
Last ObjectModification:
2016_01_14-PM-07_06_25
Theory : computation
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