Nuprl Lemma : list-if-has-value-length2
∀l:Base. l ∈ Base List supposing (||l||)↓
Proof
Definitions occuring in Statement :
length: ||as||,
list: T List,
has-value: (a)↓,
uimplies: b supposing a,
all: ∀x:A. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
length: ||as||,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strict: strict(F),
and: P ∧ Q,
implies: P ⇒ Q,
has-value: (a)↓,
uall: ∀[x:A]. B[x],
prop: ℙ,
is-exception: is-exception(t),
false: False
Lemmas referenced :
is-exception_wf,
exception-not-value,
base_wf,
has-value_wf_base,
int-value-type,
value-type-has-value,
list-if-has-value-list_ind
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
dependent_functionElimination,
thin,
baseClosed,
sqequalRule,
independent_isectElimination,
independent_pairFormation,
callbyvalueAdd,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
productElimination,
isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
addExceptionCases,
axiomSqleEquality,
sqleReflexivity,
independent_functionElimination,
voidElimination,
axiomEquality
Latex:
\mforall{}l:Base. l \mmember{} Base List supposing (||l||)\mdownarrow{}
Date html generated:
2016_05_14-AM-06_33_26
Last ObjectModification:
2016_01_14-PM-08_23_33
Theory : list_0
Home
Index