Nuprl Lemma : append_comm_1
∀T:Type. ∀a:T. ∀as:T List. ((as @ [a]) ≡(T) ([a] @ as))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
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_induction,
permr_wf,
append_wf,
cons_wf,
nil_wf,
list_ind_nil_lemma,
istype-void,
list_ind_cons_lemma,
list_wf,
istype-universe,
permr_weakening,
permr_functionality_wrt_permr,
cons_functionality_wrt_permr,
hd_two_swap_permr
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
because_Cache,
hypothesis,
universeIsType,
independent_functionElimination,
isect_memberEquality_alt,
voidElimination,
rename,
inhabitedIsType,
universeEquality,
productElimination
Latex:
\mforall{}T:Type. \mforall{}a:T. \mforall{}as:T List. ((as @ [a]) \mequiv{}(T) ([a] @ as))
Date html generated:
2019_10_16-PM-01_01_04
Last ObjectModification:
2018_10_08-AM-10_16_22
Theory : perms_2
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