Nuprl Lemma : spread-ispair-spread
∀[t,B:Top]. (let x,y = t in B[x;y] ~ if t is a pair then let x,y = t in B[x;y] otherwise ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
ispair: if z is a pair then a otherwise b,
spread: spread def,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
top: Top
Lemmas referenced :
bottom-sqle,
top_wf,
has-value-implies-dec-ispair-2,
is-exception_wf,
has-value_wf_base,
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,
sqleReflexivity,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
spreadExceptionCases,
axiomSqleEquality,
exceptionSqequal,
callbyvalueIspair,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
ispairExceptionCases,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[t,B:Top]. (let x,y = t in B[x;y] \msim{} if t is a pair then let x,y = t in B[x;y] otherwise \mbot{})
Date html generated:
2016_05_13-PM-03_46_27
Last ObjectModification:
2016_01_14-PM-07_11_11
Theory : call!by!value_2
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