Nuprl Lemma : append-cancellation
∀[T:Type]. ∀[as,as',bs,cs:T List].
(cs = bs ∈ (T List)) supposing (((as @ cs) = (as' @ bs) ∈ (T List)) and (||as|| = ||as'|| ∈ ℤ))
Proof
Definitions occuring in Statement :
length: ||as||,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
or: P ∨ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
append_wf,
list_wf,
length_wf,
equal_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
general-append-cancellation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
inlFormation,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
productElimination,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,as',bs,cs:T List].
(cs = bs) supposing (((as @ cs) = (as' @ bs)) and (||as|| = ||as'||))
Date html generated:
2016_05_14-AM-07_39_16
Last ObjectModification:
2016_01_15-AM-08_36_52
Theory : list_1
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