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Proof step 2 from proof Diffie-Hellman (previous step)

prime(j), i < j, i1 < j, i3 < j, 1 < i, 0 < i, 1 < j, 0 < i1, 0 < i3, 0 < j ⊦ (i ^ i1 |%| j) ^ i3 |%| j = (i ^ i3 |%| j) ^ i1 |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i0 ∧ 0 < j → (i |%| j) ^ i0 |%| j = i ^ i0 |%| j
Proof step 4:
0 ≤ i3 ∧ 0 < j, prime(j), i < j, i1 < j, i3 < j, 1 < i, 0 < i, 1 < j, 0 < i1, 0 < i3, 0 < j ⊦ (i ^ i1) ^ i3 |%| j = (i ^ i3 |%| j) ^ i1 |%| j

Rule argument

spec: inst: name: mod-pot-pot seq: ⊦ 0 ≤ i0 ∧ 0 < j → (i |%| j) ^ i0 |%| j = i ^ i0 |%| j subst: [i0, j, i] → [i3, j, i ^ i1] flags: rewrite, current

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i3, j, i ^ i1