Nuprl Lemma : max_w_unit_l_tree_wf
∀[T:Type]. ∀[u1,u2:T?]. ∀[f:T ⟶ ℤ]. (max_w_unit_l_tree(u1;u2;f) ∈ T?)
Proof
Definitions occuring in Statement :
max_w_unit_l_tree: max_w_unit_l_tree(u1;u2;f),
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
max_w_unit_l_tree: max_w_unit_l_tree(u1;u2;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
max_w_ord_wf,
unit_wf2,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
because_Cache,
lambdaFormation,
unionElimination,
inlEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
intEquality,
isect_memberEquality,
unionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[u1,u2:T?]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. (max\_w\_unit\_l\_tree(u1;u2;f) \mmember{} T?)
Date html generated:
2019_10_31-AM-06_25_42
Last ObjectModification:
2018_08_21-PM-02_01_02
Theory : labeled!trees
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