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Theorem mod-pot-pot

⊦ 0 ≤ i0 ∧ 0 < j → (i |%| j) ^ i0 |%| j = i ^ i0 |%| j

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: Diffie-Hellman, RSA-decrypt-ij-vars,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 15
Used lemmas: mod-mod, mod-mult-law,
Used spec theorems:
- int-pot/Pot-pos
- int-pot/succ
Used simplifier rules:
- int-abs/lels
- int-abs/anti
- oelem/intlista/lel
- int-pot/Pot-zero
- int-abs/forward-le-05
- int-abs/sub-pred
- int-abs/elim-sub
- int-abs/forward-le-01
- int-abs/numleledel-01
- int-abs/mone-06
- int-abs/numls-02
- int-abs/numle-02
- int-abs/zero-gels-04
- intnat/rax-04
- int-basic2/add-a
- int-basic2/add-c
- nat-basic2/s
- intnat/labs
- int-abs/absle
- oelem/intlista/irreflexivity
- nat-basic2/a
- nat-basic2/c