Nuprl Lemma : sq_stable__bs_tree_ordered
∀[E:Type]. ∀cmp:comparison(E). ∀tr:bs_tree(E). SqStable(bs_tree_ordered(E;cmp;tr))
Proof
Definitions occuring in Statement :
bs_tree_ordered: bs_tree_ordered(E;cmp;tr),
bs_tree: bs_tree(E),
comparison: comparison(T),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
bs_tree_ordered: bs_tree_ordered(E;cmp;tr),
bst_null: bst_null(),
bs_tree_ind: bs_tree_ind,
bst_leaf: bst_leaf(value),
bst_node: bst_node(left;value;right),
prop: ℙ,
and: P ∧ Q,
comparison: comparison(T),
sq_stable: SqStable(P),
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
comparison_wf,
squash_wf,
member-less_than,
sq_stable__less_than,
sq_stable__all,
less_than_wf,
member_bs_tree_wf,
all_wf,
sq_stable__and,
decidable__true,
true_wf,
sq_stable_from_decidable,
bs_tree_wf,
bs_tree_ordered_wf,
sq_stable_wf,
bs_tree-induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
independent_functionElimination,
because_Cache,
isect_memberEquality,
productEquality,
functionEquality,
natural_numberEquality,
applyEquality,
setElimination,
rename,
introduction,
dependent_functionElimination,
productElimination,
independent_pairEquality,
independent_isectElimination,
universeEquality
Latex:
\mforall{}[E:Type]. \mforall{}cmp:comparison(E). \mforall{}tr:bs\_tree(E). SqStable(bs\_tree\_ordered(E;cmp;tr))
Date html generated:
2016_05_15-PM-01_51_10
Last ObjectModification:
2016_04_08-AM-00_56_13
Theory : tree_1
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