[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 6 from proof mkDecimal-maxScale-le (previous step)

maxScale(i) ≤ abs(j), maxScale(i) ≤ abs(j) ⊦ i / 10 ^ maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).int ∧ mkDecimal(i, j).scale = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).scale

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = abs(j) - maxScale(i)
Proof step 8:
maxScale(i) ≤ abs(j), maxScale(i) ≤ abs(j), maxScale(i) ≤ abs(j) ⊦ i / 10 ^ maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).int ∧ abs(j) - maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).scale

Rule argument

spec: inst: name: mkDecimal-maxScale-le-scale seq: ⊦ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = abs(j) - maxScale(i) subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i