Nuprl Lemma : accum_split_one_one
∀[A,T:Type]. ∀[x:A]. ∀[g:(T List × A) ⟶ A]. ∀[f:(T List × A) ⟶ 𝔹]. ∀[X,Y:T List].
X = Y ∈ (T List) supposing accum_split(g;x;f;X) = accum_split(g;x;f;Y) ∈ ((T List × A) List × T List × A)
Proof
Definitions occuring in Statement :
accum_split: accum_split(g;x;f;L),
list: T List,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
top: Top,
pi1: fst(t),
pi2: snd(t),
guard: {T}
Lemmas referenced :
accum_split_inverse,
accum_split_wf,
list_wf,
set_wf,
is_accum_splitting_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
equal_wf,
pi2_wf,
bool_wf,
append_wf,
concat_wf,
map_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
cumulativity,
functionExtensionality,
applyEquality,
productEquality,
hypothesis,
sqequalRule,
lambdaEquality,
spreadEquality,
productElimination,
independent_pairEquality,
lambdaFormation,
setElimination,
rename,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
setEquality,
axiomEquality,
functionEquality,
universeEquality,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}[A,T:Type]. \mforall{}[x:A]. \mforall{}[g:(T List \mtimes{} A) {}\mrightarrow{} A]. \mforall{}[f:(T List \mtimes{} A) {}\mrightarrow{} \mBbbB{}]. \mforall{}[X,Y:T List].
X = Y supposing accum\_split(g;x;f;X) = accum\_split(g;x;f;Y)
Date html generated:
2016_10_25-AM-11_10_44
Last ObjectModification:
2016_07_12-AM-07_17_16
Theory : general
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