Nuprl Lemma : length-wf-has-value
∀[l:Base]. ||l|| ∈ ℤ supposing (||l||)↓
Proof
Definitions occuring in Statement :
length: ||as||,
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
length: ||as||,
so_lambda: λ2x.t[x],
so_apply: x[s],
strict1: strict1(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
or: P ∨ Q,
squash: ↓T,
has-value: (a)↓,
false: False,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
top: Top
Lemmas referenced :
has-value-monotonic,
sqle_wf_base,
general_add_assoc,
exception-not-value,
int-value-type,
value-type-has-value,
is-exception_wf,
sqle-list_ind,
base_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
isect_memberEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
inrFormation,
imageMemberEquality,
callbyvalueAdd,
productElimination,
addExceptionCases,
exceptionSqequal,
imageElimination,
sqleReflexivity,
independent_functionElimination,
voidElimination,
voidEquality,
sqleRule,
divergentSqle,
dependent_functionElimination
Latex:
\mforall{}[l:Base]. ||l|| \mmember{} \mBbbZ{} supposing (||l||)\mdownarrow{}
Date html generated:
2016_05_14-AM-06_33_10
Last ObjectModification:
2016_01_14-PM-08_23_45
Theory : list_0
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