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Bip32-ext-priv-key

Bip32-ext-priv-key->key

Get the key field from a bip32-ext-priv-key.

Signature
(bip32-ext-priv-key->key x) → key
Arguments: x — Guard (bip32-ext-priv-key-p x).
Returns: key — Type (secp256k1-priv-key-p key).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: bip32-ext-priv-key->key$inline

(defun bip32-ext-priv-key->key$inline (x)
  (declare (xargs :guard (bip32-ext-priv-key-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'bip32-ext-priv-key->key))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (ecurve::secp256k1-priv-key-fix (std::da-nth 0 x)))
         :exec (std::da-nth 0 x))))

Theorem: secp256k1-priv-key-p-of-bip32-ext-priv-key->key

(defthm secp256k1-priv-key-p-of-bip32-ext-priv-key->key
  (b* ((key (bip32-ext-priv-key->key$inline x)))
    (secp256k1-priv-key-p key))
  :rule-classes :rewrite)

Theorem: bip32-ext-priv-key->key$inline-of-bip32-ext-priv-key-fix-x

(defthm bip32-ext-priv-key->key$inline-of-bip32-ext-priv-key-fix-x
  (equal (bip32-ext-priv-key->key$inline (bip32-ext-priv-key-fix x))
         (bip32-ext-priv-key->key$inline x)))

Theorem: bip32-ext-priv-key->key$inline-bip32-ext-priv-key-equiv-congruence-on-x

(defthm
 bip32-ext-priv-key->key$inline-bip32-ext-priv-key-equiv-congruence-on-x
 (implies (bip32-ext-priv-key-equiv x x-equiv)
          (equal (bip32-ext-priv-key->key$inline x)
                 (bip32-ext-priv-key->key$inline x-equiv)))
 :rule-classes :congruence)