Nuprl Lemma : spreadcons_wf
∀[T,A:Type]. ∀[t:T ⟶ (T List) ⟶ A]. ∀[l:T List]. let a.b = l in t[a;b] ∈ A supposing 0 < ||l||
Proof
Definitions occuring in Statement :
spreadcons: spreadcons,
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
spreadcons: spreadcons,
all: ∀x:A. B[x],
or: P ∨ Q,
nil: [],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
length: ||as||,
list_ind: list_ind,
it: ⋅,
false: False,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
cons: [a / b],
so_apply: x[s1;s2]
Lemmas referenced :
list-cases,
equal_wf,
product_subtype_list,
less_than_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
voidElimination,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
promote_hyp,
hypothesis_subsumption,
applyEquality,
functionExtensionality,
cumulativity,
axiomEquality,
natural_numberEquality,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}[t:T {}\mrightarrow{} (T List) {}\mrightarrow{} A]. \mforall{}[l:T List]. let a.b = l in t[a;b] \mmember{} A supposing 0 < ||l||
Date html generated:
2017_09_29-PM-05_50_50
Last ObjectModification:
2017_05_10-PM-02_29_10
Theory : ML
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