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Proof step 12 from proof mult-ls (previous step)

0 < i ⊦ mkDecimal(i * i1, abs(i0) + abs(i2)) < mkDecimal(i * i3, abs(i0) + abs(i4)) ↔ mkDecimal(i1, i2) < mkDecimal(i3, i4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ mkDecimal(i, j) < mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j)
Proof step 14:
0 < i ⊦ (i * i1) * 10 ^ abs(abs(i0) + abs(i4)) < (i * i3) * 10 ^ abs(abs(i0) + abs(i2)) ↔ mkDecimal(i1, i2) < mkDecimal(i3, i4)

Rule argument

spec: inst: name: less-def-any seq: ⊦ mkDecimal(i, j) < mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j) subst: [j0, i0, j, i] → [abs(i0) + abs(i4), i * i3, abs(i0) + abs(i2), i * i1] flags: rewrite, current

Additional information

Used terms: abs(i0) + abs(i4), i * i3, abs(i0) + abs(i2), i * i1