Nuprl Lemma : min_l_tree_wf
∀[L,T:Type]. ∀t:l_tree(L;T). ∀f:T ⟶ ℤ. (min_l_tree(t;f) ∈ T?)
Proof
Definitions occuring in Statement :
min_l_tree: min_l_tree(t;f),
l_tree: l_tree(L;T),
uall: ∀[x:A]. B[x],
all: ∀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,
all: ∀x:A. B[x],
min_l_tree: min_l_tree(t;f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5]
Lemmas referenced :
l_tree_ind_wf_simple,
top_wf,
unit_wf2,
l_tree_covariant,
it_wf,
min_w_unit_l_tree_wf,
l_tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
unionEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
inrEquality,
inlEquality,
functionEquality,
intEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[L,T:Type]. \mforall{}t:l\_tree(L;T). \mforall{}f:T {}\mrightarrow{} \mBbbZ{}. (min\_l\_tree(t;f) \mmember{} T?)
Date html generated:
2016_05_16-AM-08_44_07
Last ObjectModification:
2015_12_28-PM-06_41_35
Theory : labeled!trees
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