Nuprl Lemma : not-ispair
∀[t,a,b:Base].
∀[x,y:Top]. (if t is a pair then x otherwise y ~ y) supposing if t is a pair then inl a otherwise inr b ~ inr b
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,
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,
false: False,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
top: Top
Lemmas referenced :
base_wf,
top_wf,
not_zero_sqequal_one,
subtype_rel_self,
subtype_base_sq,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
hypothesis,
divergentSqle,
sqleReflexivity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
baseClosed,
callbyvalueIspair,
ispairCases,
because_Cache,
hypothesisEquality,
instantiate,
independent_isectElimination,
independent_functionElimination,
voidElimination,
promote_hyp,
dependent_functionElimination,
sqequalAxiom,
isect_memberEquality,
voidEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[t,a,b:Base].
\mforall{}[x,y:Top]. (if t is a pair then x otherwise y \msim{} y)
supposing if t is a pair then inl a otherwise inr b \msim{} inr b
Date html generated:
2016_05_13-PM-03_22_01
Last ObjectModification:
2016_01_14-PM-06_47_11
Theory : call!by!value_1
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