Nuprl Lemma : ispair-implies
∀[t:Base]. (t ~ <fst(t), snd(t)>) supposing ((↑ispair(t)) and (t)↓)
Proof
Definitions occuring in Statement :
has-value: (a)↓,
assert: ↑b,
bfalse: ff,
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
ispair: if z is a pair then a otherwise b,
pair: <a, b>,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
pi1: fst(t),
pi2: snd(t),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
implies: P ⇒ Q,
prop: ℙ,
top: Top,
bfalse: ff,
false: False
Lemmas referenced :
base_wf,
ispair-bool-if-has-value,
assert_wf,
false_wf,
top_wf,
true_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
ispairCases,
divergentSqle,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
baseClosed,
hypothesisEquality,
sqequalRule,
lambdaFormation,
sqequalAxiom,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
independent_functionElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[t:Base]. (t \msim{} <fst(t), snd(t)>) supposing ((\muparrow{}ispair(t)) and (t)\mdownarrow{})
Date html generated:
2016_05_13-PM-03_27_24
Last ObjectModification:
2016_01_14-PM-06_43_21
Theory : call!by!value_1
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