Nuprl Lemma : lapp_fact_b
∀T:Type. ∀as:T List. (as = (Π 0 ≤ i < ||as||. [as[i]]) ∈ (T List))
Proof
Definitions occuring in Statement :
lapp_imon: <T List,@>,
select: L[n],
length: ||as||,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
mon_itop: Π lb ≤ i < ub. E[i]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
grp_car: |g|,
pi1: fst(t),
lapp_imon: <T List,@>,
list: T List,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q
Lemmas referenced :
list_wf,
lapp_fact_a,
equal_wf,
squash_wf,
true_wf,
istype-universe,
mon_for_eq_itop,
lapp_imon_wf,
cons_wf,
nil_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
universeEquality,
dependent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
because_Cache,
sqequalRule,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}T:Type. \mforall{}as:T List. (as = (\mPi{} 0 \mleq{} i < ||as||. [as[i]]))
Date html generated:
2019_10_16-PM-01_03_11
Last ObjectModification:
2018_10_08-AM-11_41_08
Theory : list_2
Home
Index