Nuprl Lemma : ispair-pair
∀[t,x,y:Base]. t ∈ Top × Top supposing if t is a pair then inl x otherwise inr y ~ inl x
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
ispair: if z is a pair then a otherwise b,
member: t ∈ T,
product: x:A × B[x],
inr: inr x ,
inl: inl x,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
implies: P ⇒ Q,
top: Top,
false: False
Lemmas referenced :
not_zero_sqequal_one,
base_wf,
top_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalRule,
divergentSqle,
sqleReflexivity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
callbyvalueIspair,
ispairCases,
hypothesisEquality,
lambdaFormation,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
sqequalAxiom,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
addLevel,
levelHypothesis,
promote_hyp
Latex:
\mforall{}[t,x,y:Base]. t \mmember{} Top \mtimes{} Top supposing if t is a pair then inl x otherwise inr y \msim{} inl x
Date html generated:
2016_05_13-PM-03_22_00
Last ObjectModification:
2016_01_14-PM-06_47_20
Theory : call!by!value_1
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