Nuprl Lemma : compat-append2
∀[T:Type]. ∀as,cs,bs,ds:T List. (as @ bs || cs @ ds ⇒ bs || ds supposing as = cs ∈ (T List))
Proof
Definitions occuring in Statement :
compat: l1 || l2,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
so_apply: x[s],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
and: P ∧ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
guard: {T}
Lemmas referenced :
list_induction,
all_wf,
list_wf,
compat_wf,
append_wf,
equal_wf,
list_ind_nil_lemma,
and_wf,
squash_wf,
true_wf,
equal-wf-base-T,
nil_wf,
cons_wf,
null_nil_lemma,
btrue_wf,
null_wf3,
subtype_rel_list,
top_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
equal-wf-T-base,
list_ind_cons_lemma,
compat-cons,
reduce_tl_cons_lemma,
tl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
because_Cache,
functionEquality,
isectEquality,
independent_functionElimination,
rename,
dependent_functionElimination,
universeEquality,
axiomEquality,
addLevel,
hyp_replacement,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
independent_pairFormation,
equalityTransitivity,
applyLambdaEquality,
setElimination,
productElimination,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
levelHypothesis,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}as,cs,bs,ds:T List. (as @ bs || cs @ ds {}\mRightarrow{} bs || ds supposing as = cs)
Date html generated:
2018_05_21-PM-06_46_30
Last ObjectModification:
2017_07_26-PM-04_56_16
Theory : general
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