Nuprl Lemma : bs_tree_ordered_wf
∀[E:Type]. ∀[cmp:comparison(E)]. ∀[tr:bs_tree(E)]. (bs_tree_ordered(E;cmp;tr) ∈ ℙ)
Proof
Definitions occuring in Statement :
bs_tree_ordered: bs_tree_ordered(E;cmp;tr),
bs_tree: bs_tree(E),
comparison: comparison(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bs_tree_ordered: bs_tree_ordered(E;cmp;tr),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
and: P ∧ Q,
implies: P ⇒ Q,
comparison: comparison(T),
all: ∀x:A. B[x],
so_apply: x[s1;s2;s3;s4;s5]
Lemmas referenced :
comparison_wf,
bs_tree_wf,
less_than_wf,
member_bs_tree_wf,
all_wf,
true_wf,
bs_tree_ind_wf_simple
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
universeEquality,
hypothesis,
lambdaEquality,
because_Cache,
productEquality,
functionEquality,
natural_numberEquality,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
dependent_functionElimination
Latex:
\mforall{}[E:Type]. \mforall{}[cmp:comparison(E)]. \mforall{}[tr:bs\_tree(E)]. (bs\_tree\_ordered(E;cmp;tr) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-01_51_08
Last ObjectModification:
2016_04_07-PM-07_03_12
Theory : tree_1
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