Nuprl Lemma : bs_tree_insert_wf1
∀[E:Type]. ∀[cmp:comparison(E)]. ∀[x:E]. ∀[tr:bs_tree(E)]. (bs_tree_insert(cmp;x;tr) ∈ bs_tree(E))
Proof
Definitions occuring in Statement :
bs_tree_insert: bs_tree_insert(cmp;x;tr),
bs_tree: bs_tree(E),
comparison: comparison(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bs_tree_insert: bs_tree_insert(cmp;x;tr),
so_lambda: λ2x.t[x],
has-value: (a)↓,
uimplies: b supposing a,
comparison: comparison(T),
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
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],
all: ∀x:A. B[x]
Lemmas referenced :
bs_tree_ind_wf_simple,
bs_tree_wf,
bst_leaf_wf,
value-type-has-value,
int-value-type,
top_wf,
less_than_wf,
bst_node_wf,
bst_null_wf,
comparison_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
callbyvalueReduce,
intEquality,
independent_isectElimination,
applyEquality,
setElimination,
rename,
natural_numberEquality,
lessCases,
independent_pairFormation,
baseClosed,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
axiomSqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
imageElimination,
productElimination,
independent_functionElimination,
axiomEquality,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[E:Type]. \mforall{}[cmp:comparison(E)]. \mforall{}[x:E]. \mforall{}[tr:bs\_tree(E)]. (bs\_tree\_insert(cmp;x;tr) \mmember{} bs\_tree(E))
Date html generated:
2019_10_15-AM-10_47_13
Last ObjectModification:
2018_08_20-PM-09_41_22
Theory : tree_1
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