Nuprl Lemma : is-list-prop2
∀[T:Type]. ∀[t:T List]. (is-list(t))↓
Proof
Definitions occuring in Statement :
is-list: is-list(t),
list: T List,
has-value: (a)↓,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
bool: 𝔹,
so_apply: x[s],
implies: P ⇒ Q,
is-list: is-list(t),
has-value: (a)↓,
nil: [],
it: ⋅,
btrue: tt,
all: ∀x:A. B[x],
cons: [a / b],
pi2: snd(t),
prop: ℙ,
list: T List
Lemmas referenced :
is-list_wf,
is-exception_wf,
has-value_wf_base,
list_wf,
unit_wf2,
union-value-type,
bool_wf,
has-value_wf-partial,
list_induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_isectElimination,
because_Cache,
cumulativity,
independent_functionElimination,
divergentSqle,
sqleReflexivity,
baseClosed,
lambdaFormation,
rename,
setElimination,
dependent_functionElimination,
axiomSqleEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:T List]. (is-list(t))\mdownarrow{}
Date html generated:
2016_05_15-PM-10_07_40
Last ObjectModification:
2016_01_16-PM-04_09_47
Theory : eval!all
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