Nuprl Lemma : test-spread-normalize
∀[a,B:Top]. (let x,y = a in if a is a pair then B[a] otherwise 2 ~ let x,y = a in B[<x, y>])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
ispair: if z is a pair then a otherwise b,
spread: spread def,
pair: <a, b>,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
top_wf,
equal_wf,
has-value_wf_base,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
voidElimination,
voidEquality,
lambdaFormation,
sqequalSqle,
divergentSqle,
callbyvalueSpread,
productEquality,
productElimination,
sqleReflexivity,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
spreadExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed
Latex:
\mforall{}[a,B:Top]. (let x,y = a in if a is a pair then B[a] otherwise 2 \msim{} let x,y = a in B[<x, y>])
Date html generated:
2017_04_14-AM-07_35_21
Last ObjectModification:
2017_02_27-PM-03_08_12
Theory : fun_1
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