Nuprl Lemma : inl-eta
∀[x:Top]. ∀d:Top + Top. d ~ inl outl(d) supposing d = (inl x) ∈ (Top + Top)
Proof
Definitions occuring in Statement :
outl: outl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
inl: inl x,
union: left + right,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
outl: outl(x),
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
true: True,
false: False,
prop: ℙ
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
equal_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
unionElimination,
thin,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
lambdaEquality,
natural_numberEquality,
because_Cache,
hypothesis,
instantiate,
lemma_by_obid,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
promote_hyp,
sqequalAxiom,
unionEquality,
hypothesisEquality,
inlEquality,
isect_memberEquality
Latex:
\mforall{}[x:Top]. \mforall{}d:Top + Top. d \msim{} inl outl(d) supposing d = (inl x)
Date html generated:
2016_05_13-PM-03_20_32
Last ObjectModification:
2015_12_26-AM-09_10_49
Theory : union
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