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Dead-code-eliminator-no-loop-initializers

Proof that the DeadCodeEliminator transformation preserves the condition in which loop initialization blocks are empty.

Definitions and Theorems

Theorem: statement-noloopinitp-of-statement-dead

(defthm statement-noloopinitp-of-statement-dead
  (implies (statement-noloopinitp stmt)
           (statement-noloopinitp (statement-dead stmt))))

Theorem: statement-list-noloopinitp-of-statement-list-dead

(defthm statement-list-noloopinitp-of-statement-list-dead
 (implies (statement-list-noloopinitp stmts)
          (statement-list-noloopinitp (statement-list-dead stmts))))

Theorem: block-noloopinitp-of-block-dead

(defthm block-noloopinitp-of-block-dead
  (implies (block-noloopinitp block)
           (block-noloopinitp (block-dead block))))

Theorem: block-option-noloopinitp-of-block-option-dead

(defthm block-option-noloopinitp-of-block-option-dead
  (implies (block-option-noloopinitp block?)
           (block-option-noloopinitp (block-option-dead block?))))

Theorem: swcase-noloopinitp-of-swcase-dead

(defthm swcase-noloopinitp-of-swcase-dead
  (implies (swcase-noloopinitp case)
           (swcase-noloopinitp (swcase-dead case))))

Theorem: swcase-list-noloopinitp-of-swcase-list-dead

(defthm swcase-list-noloopinitp-of-swcase-list-dead
  (implies (swcase-list-noloopinitp cases)
           (swcase-list-noloopinitp (swcase-list-dead cases))))

Theorem: fundef-noloopinitp-of-fundef-dead

(defthm fundef-noloopinitp-of-fundef-dead
  (implies (fundef-noloopinitp fundef)
           (fundef-noloopinitp (fundef-dead fundef))))