Nuprl Lemma : bs_tree_max_wf1
∀[E:Type]. ∀[tr:bs_tree(E)]. ∀[d:E]. (bs_tree_max(tr;d) ∈ E × bs_tree(E))
Proof
Definitions occuring in Statement :
bs_tree_max: bs_tree_max(tr;d),
bs_tree: bs_tree(E),
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bs_tree_max: bs_tree_max(tr;d),
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 :
bst_node_wf,
bst_null?_wf,
ifthenelse_wf,
bst_null_wf,
bs_tree_wf,
bs_tree_ind_wf_simple
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
productEquality,
hypothesis,
independent_pairEquality,
lambdaEquality,
spreadEquality,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[E:Type]. \mforall{}[tr:bs\_tree(E)]. \mforall{}[d:E]. (bs\_tree\_max(tr;d) \mmember{} E \mtimes{} bs\_tree(E))
Date html generated:
2016_05_15-PM-01_51_39
Last ObjectModification:
2016_04_08-PM-03_21_46
Theory : tree_1
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