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Proof step 15 from proof dec2int-def-any (previous step)

i % 10 = 0, ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ i→n(i / 10) < i→n(i), j = 0, dec2int(mkDecimal(i / 10, abs(j) - 1)) = i / 10 ^ abs(j)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: dec2int-zero-01: ⊦ dec2int(mkDecimal(0, j)) = 0;%zero: j ≠ 0 ⊦ 0 / j = 0; from specification int-div%absls: ⊦ ¬ abs(i) < 0; from specification int-abs%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%abs-div10-le: ⊦ abs(i) ≤ abs(i) / 10 ↔ i = 0; from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j); from specification int-div%labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat