Nuprl Lemma : l_tree_covariant
∀[A,B,T:Type]. l_tree(A;T) ⊆r l_tree(B;T) supposing A ⊆r B
Proof
Definitions occuring in Statement :
l_tree: l_tree(L;T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Lemmas :
subtype_rel_wf,
l_tree_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
le_wf,
l_tree_size_wf,
int_seg_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
l_tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
l_tree_leaf_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
not-le-2,
subtract-is-less,
lelt_wf,
l_tree_node_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
sq_stable__le,
add-mul-special,
zero-mul,
nat_wf
\mforall{}[A,B,T:Type]. l\_tree(A;T) \msubseteq{}r l\_tree(B;T) supposing A \msubseteq{}r B
Date html generated:
2015_07_17-AM-07_41_43
Last ObjectModification:
2015_01_27-AM-09_31_21
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