Nuprl Lemma : cons_one_one
∀[T:Type]. ∀[a,a':T]. ∀[b,b':T List]. uiff([a / b] = [a' / b'] ∈ (T List);{(a = a' ∈ T) ∧ (b = b' ∈ (T List))})
Proof
Definitions occuring in Statement :
cons: [a / b],
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
squash: ↓T,
ge: i ≥ j ,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
cons_wf,
tl_wf,
equal_wf,
and_wf,
reduce_tl_cons_lemma,
top_wf,
subtype_rel_list,
length_cons_ge_one,
list_wf,
length_wf,
ge_wf,
squash_wf,
hd_wf,
reduce_hd_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
universeEquality,
because_Cache,
imageMemberEquality,
baseClosed,
dependent_set_memberEquality,
setElimination,
rename,
productElimination,
setEquality,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,a':T]. \mforall{}[b,b':T List]. uiff([a / b] = [a' / b'];\{(a = a') \mwedge{} (b = b')\})
Date html generated:
2016_05_14-AM-06_43_03
Last ObjectModification:
2016_01_14-PM-08_18_40
Theory : list_0
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