Nuprl Lemma : append_cancel
∀[A:Type]. ∀[as,bs,cs:A List]. bs = cs ∈ (A List) supposing (as @ bs) = (as @ cs) ∈ (A List)
Proof
Definitions occuring in Statement :
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
guard: {T},
and: P ∧ Q
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
equal_wf,
append_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
cons_wf,
reduce_tl_cons_lemma,
and_wf,
tl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
universeEquality,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
productElimination,
independent_isectElimination
Latex:
\mforall{}[A:Type]. \mforall{}[as,bs,cs:A List]. bs = cs supposing (as @ bs) = (as @ cs)
Date html generated:
2017_04_17-AM-08_13_18
Last ObjectModification:
2017_02_27-PM-04_39_04
Theory : list_1
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