Nuprl Lemma : valuetype__tree
∀[E:Type]. value-type(tree(E))
Proof
Definitions occuring in Statement :
tree: tree(E),
value-type: value-type(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tree: tree(E),
so_lambda: λ2x.t[x],
uimplies: b supposing a,
nat: ℕ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
value-type: value-type(T),
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
set-value-type,
treeco_wf,
has-value_wf-partial,
nat_wf,
le_wf,
int-value-type,
treeco_size_wf,
value-type_functionality,
ifthenelse_wf,
eq_atom_wf,
treeco-ext,
product-value-type,
equal-wf-base,
tree_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
intEquality,
natural_numberEquality,
because_Cache,
productEquality,
atomEquality,
instantiate,
tokenEquality,
universeEquality,
voidEquality,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[E:Type]. value-type(tree(E))
Date html generated:
2017_10_01-AM-08_30_37
Last ObjectModification:
2017_05_02-PM-02_37_37
Theory : tree_1
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