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lib: add upcast_less_unat_less 

Signed-off-by: Matthew Brecknell <Matthew.Brecknell@data61.csiro.au>
This commit is contained in:
Matthew Brecknell 2020-09-09 15:20:59 +10:00 committed by Matthew Brecknell
parent 0ba5b52d59
commit 91abdb5720
1 changed files with 12 additions and 0 deletions
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12
lib/Word_Lib/Word_Lemmas_Internal.thy
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@ -400,4 +400,16 @@ lemma le_smaller_mask:
"\<lbrakk> x \<le> mask n; n \<le> m \<rbrakk> \<Longrightarrow> x \<le> mask m"
by (erule (1) order.trans[OF _ mask_mono])
(* The strange phrasing and ordering of assumptions is to support using this as a
conditional simp rule when y is a concrete value. For example, as a simp rule,
it will solve a goal of the form:
UCAST(8 \<rightarrow> 32) x < 0x20 \<Longrightarrow> unat x < 32
This is used in an obscure corner of SimplExportAndRefine. *)
lemma upcast_less_unat_less:
assumes less: "UCAST('a \<rightarrow> 'b) x < UCAST('a \<rightarrow> 'b) (of_nat y)"
assumes len: "LENGTH('a::len) \<le> LENGTH('b::len)"
assumes bound: "y < 2 ^ LENGTH('a)"
shows "unat x < y"
by (rule unat_mono[OF less, simplified unat_ucast_up_simp[OF len] unat_of_nat_eq[OF bound]])
end