Nuprl Lemma : append_comm
∀T:Type. ∀as,bs:T List. ((as @ bs) ≡(T) (bs @ as))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_wf,
list_induction,
all_wf,
permr_wf,
append_wf,
list_ind_nil_lemma,
istype-void,
list_ind_cons_lemma,
istype-universe,
append_back_nil,
permr_reflex,
cons_wf,
permr_functionality_wrt_permr,
cons_functionality_wrt_permr,
permr_weakening,
append_assoc,
nil_wf,
append_functionality_wrt_permr,
append_comm_1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
because_Cache,
inhabitedIsType,
independent_functionElimination,
isect_memberEquality_alt,
voidElimination,
rename,
functionIsType,
productElimination
Latex:
\mforall{}T:Type. \mforall{}as,bs:T List. ((as @ bs) \mequiv{}(T) (bs @ as))
Date html generated:
2019_10_16-PM-01_01_06
Last ObjectModification:
2018_10_08-AM-09_56_51
Theory : perms_2
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