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lemma dual_set_as_map_image_code[code] :
fixes t :: "('a1 ::ccompare \<times> 'a2 :: ccompare) set_rbt"
and f1 :: "('a1 \<times> 'a2) \<Rightarrow> ('b1 :: ccompare \<times> 'b2 ::ccompare)"
and f2 :: "('a1 \<times> 'a2) \<Rightarrow> ('c1 :: ccompare \<times> 'c2 ::ccompare)"
shows "dual_set_as_map_image (RBT_set t) f1 f2 = (case ID CCOMPARE(('a1 \<times> 'a2)) of
Some _ \<Rightarrow> let mm = (RBT_Set2.fold (\<lambda> kv (m1,m2) .
( case f1 kv of (x,z) \<Rightarrow> (case Mapping.lookup m1 (x) of None \<Rightarrow> Mapping.update (x) {z} m1 | Some zs \<Rightarrow> Mapping.update (x) (Set.insert z zs) m1)
, case f2 kv of (x,z) \<Rightarrow> (case Mapping.lookup m2 (x) of None \<Rightarrow> Mapping.update (x) {z} m2 | Some zs \<Rightarrow> Mapping.update (x) (Set.insert z zs) m2)))
t
(Mapping.empty,Mapping.empty))
in (Mapping.lookup (fst mm), Mapping.lookup (snd mm)) |
None \<Rightarrow> Code.abort (STR ''dual_set_as_map_image RBT_set: ccompare = None'')
(\<lambda>_. (dual_set_as_map_image (RBT_set t) f1 f2)))" |
lemma eOp_simp6[simp]:
assumes "\<not> liftAll (\<lambda> eA. eA \<noteq> ERR) ebinp"
shows "eOp MOD delta einp ebinp = ERR" |
lemma real_to_01open_inverse_correct':
assumes "0 < r" "r < 1"
shows "real_to_01open (real_to_01open_inverse r) = r" |
lemma comm_ring_1: "OFCLASS('a, comm_ring_1_class)" |
lemma size'_char_eq_0 [simp, code]:
\<open>size_char c = 0\<close> |
lemma \<beta>_boundedness_diag_le':
fixes m :: int
shows
"- k y \<le> (m :: int) \<Longrightarrow> m \<le> k x \<Longrightarrow> x \<in> X \<Longrightarrow> y \<in> X \<Longrightarrow> Z \<subseteq> {u \<in> V. u x - u y \<le> m}
\<Longrightarrow> Approx\<^sub>\<beta> Z \<subseteq> {u \<in> V. u x - u y \<le> m}" |
lemma (in comm_ring_1) poly_divides_diff: "p divides q \<Longrightarrow> p divides (q +++ r) \<Longrightarrow> p divides r" |
lemma N_\<mu>':
assumes "i < m" "j \<le> i"
shows "(\<mu>' i j)\<^sup>2 \<le> N ^ (3 * Suc j)" |
lemma r_phi_recfn [simp]: "recfn 2 r_phi" |
lemma ftv_tyS:
fixes S::"tyS"
shows "supp S = set (ftv S)" |
lemma (in MinkowskiPrimitive) card2_either_elt1_or_elt2:
assumes "card X = 2" and "x\<in>X" and "y\<in>X" and "x\<noteq>y"
and "z\<in>X" and "z\<noteq>x"
shows "z=y" |
lemma (in carrier) openI:
"m \<in> T \<Longrightarrow> m open" |
lemma crel_vs_executeD:
assumes "crel_vs R a b" "P heap" "Q heap" "state_dp_consistency.cmem heap"
obtains x heap' where
"execute b heap = Some (x, heap')" "P heap'" "Q heap'" "state_dp_consistency.cmem heap'" "R a x" |
lemma ZFfunIdRight:
assumes a: "isZFfun f" shows "f |o| (ZFfun ( |cod|f) ( |cod|f) (\<lambda>x. x)) = f" |
lemma unfolding_monotonic:
"w \<Turnstile>\<^sub>n \<phi>[X]\<^sub>\<nu> \<Longrightarrow> w \<Turnstile>\<^sub>n (Unf \<phi>)[X]\<^sub>\<nu>" |
lemma column_Gram_Schmidt_column_k':
fixes A::"'a::{real_inner}^'n::{mod_type}^'m::{mod_type}"
assumes i_not_k: "i\<noteq>k"
shows "column i (Gram_Schmidt_column_k A (to_nat k)) = (column i A)" |
lemma size_multiset_union [simp]:
"size_multiset f (M + N::'a multiset) = size_multiset f M + size_multiset f N" |
lemma sorted_list_of_set_mono_on:
"finite A \<Longrightarrow> mono_on {..<card A} (\<lambda>n. sorted_list_of_set A ! n)" |
lemma conv_callee_parallel: "converter_of_callee (parallel_intercept callee1 callee2) (s,s')
= parallel_converter2 (converter_of_callee callee1 s) (converter_of_callee callee2 s')" |
lemma C_normal_ML_lift_ML: "C_normal\<^sub>M\<^sub>L(lift\<^sub>M\<^sub>L k v) = C_normal\<^sub>M\<^sub>L v" |
lemma HEN007_2:
"EQU001_0_ax equal &
(\<forall>X Y. mless_equal(X::'a,Y) --> quotient(X::'a,Y,Zero)) &
(\<forall>X Y. quotient(X::'a,Y,Zero) --> mless_equal(X::'a,Y)) &
(\<forall>Y Z X. quotient(X::'a,Y,Z) --> mless_equal(Z::'a,X)) &
(\<forall>Y X V3 V2 V1 Z V4 V5. quotient(X::'a,Y,V1) & quotient(Y::'a,Z,V2) & quotient(X::'a,Z,V3) & quotient(V3::'a,V2,V4) & quotient(V1::'a,Z,V5) --> mless_equal(V4::'a,V5)) &
(\<forall>X. mless_equal(Zero::'a,X)) &
(\<forall>X Y. mless_equal(X::'a,Y) & mless_equal(Y::'a,X) --> equal(X::'a,Y)) &
(\<forall>X. mless_equal(X::'a,identity)) &
(\<forall>X Y. quotient(X::'a,Y,Divide(X::'a,Y))) &
(\<forall>X Y Z W. quotient(X::'a,Y,Z) & quotient(X::'a,Y,W) --> equal(Z::'a,W)) &
(\<forall>X Y W Z. equal(X::'a,Y) & quotient(X::'a,W,Z) --> quotient(Y::'a,W,Z)) &
(\<forall>X W Y Z. equal(X::'a,Y) & quotient(W::'a,X,Z) --> quotient(W::'a,Y,Z)) &
(\<forall>X W Z Y. equal(X::'a,Y) & quotient(W::'a,Z,X) --> quotient(W::'a,Z,Y)) &
(\<forall>X Z Y. equal(X::'a,Y) & mless_equal(Z::'a,X) --> mless_equal(Z::'a,Y)) &
(\<forall>X Y Z. equal(X::'a,Y) & mless_equal(X::'a,Z) --> mless_equal(Y::'a,Z)) &
(\<forall>X Y W. equal(X::'a,Y) --> equal(Divide(X::'a,W),Divide(Y::'a,W))) &
(\<forall>X W Y. equal(X::'a,Y) --> equal(Divide(W::'a,X),Divide(W::'a,Y))) &
(\<forall>X. quotient(X::'a,identity,Zero)) &
(\<forall>X. quotient(Zero::'a,X,Zero)) &
(\<forall>X. quotient(X::'a,X,Zero)) &
(\<forall>X. quotient(X::'a,Zero,X)) &
(\<forall>Y X Z. mless_equal(X::'a,Y) & mless_equal(Y::'a,Z) --> mless_equal(X::'a,Z)) &
(\<forall>W1 X Z W2 Y. quotient(X::'a,Y,W1) & mless_equal(W1::'a,Z) & quotient(X::'a,Z,W2) --> mless_equal(W2::'a,Y)) &
(mless_equal(x::'a,y)) &
(quotient(z::'a,y,zQy)) &
(quotient(z::'a,x,zQx)) &
(~mless_equal(zQy::'a,zQx)) --> False" |
lemma ctx_subtype_v_rig_eq:
fixes v::v
assumes "replace_in_g_subtyped \<Theta> \<B> \<Gamma>' [(x,c0)] \<Gamma>" and
"\<Theta>; \<B>; \<Gamma>' \<turnstile> v \<Rightarrow> t1"
shows "\<Theta>; \<B>; \<Gamma> \<turnstile> v \<Rightarrow> t1" |
lemma finite_dom_lookup: "finite (dom (lookup t))" |
lemma inner_prod_with_row_bra_vec [simp]:
assumes "dim_vec u = dim_vec v"
shows "\<langle>u|v\<rangle> = row (bra_vec u) 0 \<bullet> v" |
lemma cycle_free_diag:
"cycle_free m n \<Longrightarrow> i \<le> n \<Longrightarrow> 0 \<le> m i i" |
lemma pickE[simp]:
assumes "length xl = length al"
and "distinct xl" and "\<And> i. i < length xl \<Longrightarrow> intT (tpOfV (xl!i)) (al!i)"
and "i < length xl"
shows "pickE xl al (xl!i) = al!i" |
lemma left_null_space_orthogonal_complement_col_space:
fixes A::"'a^'cols::{finite, wellorder}^'rows::{finite, wellorder}"
shows "left_null_space A = ROWS.v.orthogonal_complement (col_space (\<chi> i j. cnj (A $ i $ j)))" |
lemma conseq_extract_state_indep_prop:
assumes state_indep_prop:"\<forall>s \<in> P. R"
assumes to_show: "R \<Longrightarrow> \<Gamma>,\<Theta>\<turnstile>\<^sub>t\<^bsub>/F\<^esub> P c Q,A"
shows "\<Gamma>,\<Theta>\<turnstile>\<^sub>t\<^bsub>/F\<^esub> P c Q,A" |
lemma Amin_ge1Tr:"(\<forall>j\<le>(Suc n). (f j) \<in> Z\<^sub>\<infinity> \<and> z \<le> (f j)) \<longrightarrow>
z \<le> (Amin (Suc n) f)" |
lemma locally_Times:
fixes S :: "('a::metric_space) set" and T :: "('b::metric_space) set"
assumes PS: "locally P S" and QT: "locally Q T" and R: "\<And>S T. P S \<and> Q T \<Longrightarrow> R(S \<times> T)"
shows "locally R (S \<times> T)" |
lemma generate_valid_stateful_policy_IFSACS_noIFS_noACSsideeffects_imp_fullgraph:
assumes validReqs: "valid_reqs M"
and wfG: "wf_graph G"
and high_level_policy_valid: "all_security_requirements_fulfilled M G"
and edgesList: "(set edgesList) = edges G"
and no_ACS_sideeffects: "\<forall>F \<in> get_offending_flows (get_ACS M) \<lparr>nodes = nodes G, edges = edges G \<union> backflows (edges G)\<rparr>. F \<subseteq> (backflows (edges G)) - (edges G)"
and no_IFS: "get_IFS M = []"
shows "stateful_policy_to_network_graph (generate_valid_stateful_policy_IFSACS G M edgesList) = undirected G" |
lemma (in topology) closure_eq_closed:
"closure a = a \<Longrightarrow> a closed" |
lemma \<alpha>_strict[simp]: "\<alpha> (Sup {}) = bot" |
lemma member_of_to_member_in: "G \<turnstile> m member_of C \<Longrightarrow> G \<turnstile>m member_in C" |
lemma type_vector_space_on_with: "vector_space_on_with UNIV plus_S minus_S uminus_S (zero_S::'s) scale_S" |
lemma is_calls_not_is_vals [dest]: "calls es = \<lfloor>aMvs\<rfloor> \<Longrightarrow> \<not> is_vals es" |
lemma WPC_through_make_step:
assumes "set_of_graph_rules Rs" "graph (graph_of (X 0))"
and makestep: "\<forall> i. X (Suc i) = make_step selector (X i)"
and selector: "valid_selector Rs selector"
shows "Simple_WPC t Rs (\<lambda> i. graph_of (X i))" "chain (\<lambda> i. graph_of (X i))" |
lemma alpha_Tree_eqvt': "t1 =\<^sub>\<alpha> t2 \<longleftrightarrow> p \<bullet> t1 =\<^sub>\<alpha> p \<bullet> t2" |
lemma n2_type1:
"\<lbrakk>t1 \<in> Um h; t2 \<in> B h\<rbrakk> \<Longrightarrow> n2 t1 a t2 \<in> T (Suc h)" |
lemma arctic_weak_carrier:
"weak_SN_both_mono_ordered_semiring_1 (>) 1 pos_arctic" |
lemma HAInitState_HAInitStates [simp]:
"HAInitState A \<in> HAInitStates A" |
lemma invar_empty[simp]:
"invar []"
"tail_invar []" |
lemma uminus_in_iff [simp]: "(\<lambda>x. -f x) \<in> L F (g) \<longleftrightarrow> f \<in> L F (g)" |
lemma squarefree_part_nonzero [simp]: "squarefree_part n \<noteq> 0" |
lemma list_of_pdevs_perm_filter_nonzero:
"map snd (list_of_pdevs X) <~~> (filter ((\<noteq>) 0) (dense_list_of_pdevs X))" |
lemma lsu_inf_closed_var [simp]: "\<nu>\<^sup>\<natural> (\<nu>\<^sup>\<natural> x \<sqinter> \<nu>\<^sup>\<natural> y) = \<nu>\<^sup>\<natural> (x::'a::unital_quantale) \<sqinter> \<nu>\<^sup>\<natural> y" |
lemma similar_mat_wit_char_matrix: assumes wit: "similar_mat_wit A B P Q"
shows "similar_mat_wit (char_matrix A ev) (char_matrix B ev) P Q" |
lemma wf_tuple_upd_None: "wf_tuple n A xs \<Longrightarrow> A - {i} = B \<Longrightarrow> wf_tuple n B (xs[i:=None])" |
lemma pow_res_disjoint':
assumes "n > 0"
assumes "a \<in> nonzero Q\<^sub>p"
assumes "pow_res n a \<noteq> pow_res n \<one>"
shows "\<not> (\<exists>y \<in> nonzero Q\<^sub>p. a = y[^]n)" |
lemma adopt_node_wf_is_l_adopt_node_wf [instances]:
"l_adopt_node_wf type_wf known_ptr heap_is_wellformed parent_child_rel get_child_nodes
get_disconnected_nodes known_ptrs adopt_node" |
lemma comp_in_homI [intro]:
assumes "\<guillemotleft>f : a \<rightarrow> b\<guillemotright>" and "\<guillemotleft>g : b \<rightarrow> c\<guillemotright>"
shows "\<guillemotleft>g \<cdot> f : a \<rightarrow> c\<guillemotright>" |
lemma cat_smc_is_arr[slicing_simps]:
"f : a \<mapsto>\<^bsub>cat_smc \<CC>\<^esub> b \<longleftrightarrow> f : a \<mapsto>\<^bsub>\<CC>\<^esub> b" |
lemma subrel_runiq:
assumes "runiq Q" "P \<subseteq> Q"
shows "runiq P" |
lemma coeff_mod_qr_poly:
assumes "degree (f::'a mod_ring poly) \<ge> n" "degree f < 2*n" "i<n"
shows "poly.coeff (f mod qr_poly) i = poly.coeff f i - poly.coeff f (i+n)" |
lemma snd_foldl_ef_det_eq: "snd (foldl (echelon_form_of_column_k_det bezout) (n, A, 0) [0..<k])
= foldl (echelon_form_of_column_k bezout) (A, 0) [0..<k]" |
lemma lmirror_aux_LCons:
"lmirror_aux acc (LCons x xs) = LCons x (lappend (lmirror_aux LNil xs) (LCons x acc))" |
lemma card_irred_aux:
assumes "n > 0"
shows "order R^n = (\<Sum>d | d dvd n. d *
card {f. monic_irreducible_poly R f \<and> degree f = d})"
(is "?lhs = ?rhs") |
lemma add_set_commm:
"A \<otimes> B = B \<otimes> A" |
lemma "JML \<Longrightarrow> DM3 \<^bold>\<not>" |
lemma wbalanced_balance_list[simp]: "wbalanced (balance_list xs)" |
lemma length_tabulate[simp]: "length (tabulate f x n) = n" |
lemma tl_upt [simp]: "tl [m..<n] = [Suc m..<n]" |
lemma is_regular_spair_component_lt_cases:
assumes "is_regular_spair p q"
shows "component_of_term (lt (spair p q)) = component_of_term (lt p) \<or>
component_of_term (lt (spair p q)) = component_of_term (lt q)" |
lemma transpose_aux_max:
"max (Suc (length xs)) (foldr (\<lambda>xs. max (length xs)) xss 0) =
Suc (max (length xs) (foldr (\<lambda>x. max (length x - Suc 0)) (filter (\<lambda>ys. ys \<noteq> []) xss) 0))"
(is "max _ ?foldB = Suc (max _ ?foldA)") |
lemma ereal_zero_times[simp]:
fixes a b :: ereal
shows "a * b = 0 \<longleftrightarrow> a = 0 \<or> b = 0" |
lemma set_tag_name_get_tag_name_is_l_set_tag_name_get_tag_name [instances]:
"l_set_tag_name_get_tag_name type_wf get_tag_name get_tag_name_locs
set_tag_name set_tag_name_locs" |
lemma prec_eq_None_or_equal:
fixes s1 s2
assumes "s1 \<preceq> s2"
shows "s1 = None \<or> s1 = s2" |
lemma (in program) history_consistent_append_Prog\<^sub>s\<^sub>b:
assumes step: "\<theta>\<turnstile> p \<rightarrow>\<^sub>p (p', mis)"
shows "history_consistent \<theta> (hd_prog p xs) xs \<Longrightarrow> last_prog p xs = p \<Longrightarrow>
history_consistent \<theta> (hd_prog p' (xs@[Prog\<^sub>s\<^sub>b p p' mis])) (xs@[Prog\<^sub>s\<^sub>b p p' mis])" |
lemma rbt_lookup_rbt_interwk:
"\<lbrakk> rbt_sorted t1; rbt_sorted t2 \<rbrakk>
\<Longrightarrow> rbt_lookup (rbt_inter_with_key f t1 t2) k =
(case rbt_lookup t1 k of None \<Rightarrow> None
| Some v \<Rightarrow> case rbt_lookup t2 k of None \<Rightarrow> None
| Some w \<Rightarrow> Some (f k v w))" |
lemma apply_cltn2_left_abs:
assumes "v \<noteq> 0"
shows "apply_cltn2 (proj2_abs v) C = proj2_abs (v v* cltn2_rep C)" |
lemma X: "\<not> (\<tau> \<Turnstile> (invalid and B))" |
lemma "((x :: 32 word) >> 3) AND 7 = (x AND 56) >> 3" |
lemma cl_op_prop_var [iff]: "(cl_op (x \<squnion> cl_op y) = cl_op y) = (cl_op (x::'a::clattice_with_clop) \<le> cl_op y)" |
lemma uint_split_asm:
"P (uint x) = (\<nexists>i. word_of_int i = x \<and> 0 \<le> i \<and> i < 2^LENGTH('a) \<and> \<not> P i)"
for x :: "'a::len word" |
lemma init_tr_wf: "wf_tr M (init_tr M)" |
lemma p2_ident: "int (CARD('a) - 2) = p - 2" |
lemma bind_case_contract_cong [fundef_cong]:
assumes "x = x'"
and "\<And>a. x = Method a \<Longrightarrow> f a s = f' a s"
and "\<And>a. x = Var a \<Longrightarrow> g a s = g' a s"
shows "(case x of (Method a) \<Rightarrow> f a | (Var a) \<Rightarrow> g a) s
= (case x' of (Method a) \<Rightarrow> f' a | (Var a) \<Rightarrow> g' a) s" |
lemma msed_map_invL:
assumes "image_mset f (add_mset a M) = N"
shows "\<exists>N1. N = add_mset (f a) N1 \<and> image_mset f M = N1" |
lemma vote_setD:
"rv \<in> vote_set v_f {a} \<Longrightarrow> v_f (fst rv) a = Some (snd rv)" |
lemma im_len_eq_iff: "\<^bold>|u\<^bold>| = \<^bold>|f u\<^bold>| \<longleftrightarrow> (\<forall> c. c \<in> set u \<longrightarrow> \<^bold>|f [c]\<^bold>| = 1)" |
lemma ya2'_parts_imp_ya1'_parts [rule_format]:
"[| evs \<in> ya; B \<notin> bad |] ==>
Ciph B \<lbrace>Agent A, Nonce NA, Nonce NB\<rbrace> \<in> parts (spies evs) \<longrightarrow>
\<lbrace>Agent A, Nonce NA\<rbrace> \<in> spies evs" |
lemma undeclared_not_declared:
"G\<turnstile> memberid m undeclared_in C \<Longrightarrow> \<not> G\<turnstile> m declared_in C" |
lemma stopping_timeD: "stopping_time F T \<Longrightarrow> Measurable.pred (F t) (\<lambda>x. T x \<le> t)" |
lemma (in encoding) enc_preserves_pred_iff_source_target_rel_preserves_pred:
fixes Pred :: "('procS, 'procT) Proc \<Rightarrow> bool"
shows "enc_preserves_pred Pred
= (\<exists>Rel. (\<forall>S. (SourceTerm S, TargetTerm (\<lbrakk>S\<rbrakk>)) \<in> Rel) \<and> rel_preserves_pred Rel Pred)"
and "enc_preserves_pred Pred = (\<exists>Rel. (\<forall>S. (SourceTerm S, TargetTerm (\<lbrakk>S\<rbrakk>)) \<in> Rel)
\<and> rel_preserves_pred Rel Pred \<and> preorder Rel)" |
lemma fM_rel_inv[intro]:
notes fun_upd_apply[simp]
shows
"\<lbrace> LSTP (fM_rel_inv \<^bold>\<and> tso_store_inv) \<rbrace> sys \<lbrace> LSTP fM_rel_inv \<rbrace>" |
lemma degree_pos_iff: "MPoly_Type.degree p x > 0 \<longleftrightarrow> x \<in> vars p" |
lemma partitions_imp_finite_elements:
assumes "p partitions n"
shows "finite {i. 0 < p i}" |
lemma (in group) subgroup_generated_minimal:
"\<lbrakk>subgroup H G; S \<subseteq> H\<rbrakk> \<Longrightarrow> carrier(subgroup_generated G S) \<subseteq> H" |
lemma measurable_on_scaleR_const:
assumes f: "f measurable_on S"
shows "(\<lambda>x. c *\<^sub>R f x) measurable_on S" |
lemma signed_take_bit_Suc_bit0 [simp]:
\<open>signed_take_bit (Suc n) (numeral (Num.Bit0 k)) = signed_take_bit n (numeral k) * (2 :: int)\<close> |
lemma add_multiple_rows_index_unchanged [simp]:
"i < dim_row A \<Longrightarrow> j < dim_col A \<Longrightarrow> k \<noteq> i \<Longrightarrow> add_multiple_rows a k ls A $$ (i,j) = A $$(i,j)" |
lemma check_indices_state: assumes "\<not> \<U> s \<Longrightarrow> \<Turnstile>\<^sub>n\<^sub>o\<^sub>l\<^sub>h\<^sub>s s" "\<not> \<U> s \<Longrightarrow> \<diamond> s" "\<not> \<U> s \<Longrightarrow> \<triangle> (\<T> s)" "\<not> \<U> s \<Longrightarrow> \<nabla> s"
shows "indices_state (check s) = indices_state s" |
lemma e_approx_32: "\<bar>exp(1) - 5837465777 / 2147483648\<bar> \<le> (inverse(2 ^ 32)::real)" |
lemma eq_E_simple_3[PLM]:
"[(x \<^bold>= y) \<^bold>\<equiv> ((\<lparr>O!,x\<rparr> \<^bold>& \<lparr>O!,y\<rparr> \<^bold>& \<^bold>\<box>(\<^bold>\<forall>F . \<lparr>F,x\<rparr> \<^bold>\<equiv> \<lparr>F,y\<rparr>))
\<^bold>\<or> (\<lparr>A!,x\<rparr> \<^bold>& \<lparr>A!,y\<rparr> \<^bold>& \<^bold>\<box>(\<^bold>\<forall>F. \<lbrace>x,F\<rbrace> \<^bold>\<equiv> \<lbrace>y,F\<rbrace>))) in v]" |
lemma inf_continuous_and[order_continuous_intros]:
"inf_continuous P \<Longrightarrow> inf_continuous Q \<Longrightarrow> inf_continuous (\<lambda>x. P x \<and> Q x)" |
lemma from_nat_suc:
shows "from_nat (j + 1) = from_nat j + 1" |
lemma blinfun_compose_diff_right: "f o\<^sub>L (g - h) = (f o\<^sub>L g) - (f o\<^sub>L h)" |
lemma weight_return_pmf_None [simp]: "weight_spmf (return_pmf None) = 0" |
theorem routing_ipassmt_wi:
assumes vpfx: "valid_prefixes tbl"
shows
"output_iface (routing_table_semantics tbl k) = output_port \<longleftrightarrow>
(\<exists>ip_range. k \<in> wordinterval_to_set ip_range \<and> (output_port, ip_range) \<in> set (routing_ipassmt_wi tbl))" |
lemma bulkload_Mapping [code]:
"Mapping.bulkload vs = Mapping (RBT.bulkload (List.map (\<lambda>n. (n, vs ! n)) [0..<length vs]))" |
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