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Proof step 10 from proof less-totality (previous step)

⊦ mkDecimal(i, abs(i0)) = mkDecimal(i1, abs(i2)), mkDecimal(i1, abs(i2)) < mkDecimal(i, abs(i0)), mkDecimal(i, abs(i0)) < mkDecimal(i1, abs(i2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 12:
0 ≤ abs(i2) ⊦ mkDecimal(i * 10 ^ abs(i2), abs(abs(i0)) + abs(i2)) = mkDecimal(i1, abs(i2)), mkDecimal(i1, abs(i2)) < mkDecimal(i * 10 ^ abs(i2), abs(abs(i0)) + abs(i2)), mkDecimal(i * 10 ^ abs(i2), abs(abs(i0)) + abs(i2)) < mkDecimal(i1, abs(i2))

Rule argument

spec: decimal inst: name: mkDecimal-enlarge seq: ⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0) subst: [j0, j, i] → [abs(i2), abs(i0), i] flags: rewrite

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: abs(i2), abs(i0), i