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Proof step 50 from proof sub-def-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(0) + i→n(i0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ j = 0, mkDecimal(0, 0) - mkDecimal(i0, j0) = mkDecimal(~(i0 * 10 ^ abs(j)), abs(j) + abs(j0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ dec_i - dec_j = mkDecimal(dec_i.int * 10 ^ dec_j.scale - dec_j.int * 10 ^ dec_i.scale, dec_i.scale + dec_j.scale)
Proof step 52:
∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(0) + i→n(i0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ j = 0, mkDecimal (mkDecimal(0, 0).int * 10 ^ mkDecimal(i0, j0).scale - mkDecimal(i0, j0).int * 10 ^ mkDecimal(0, 0).scale, mkDecimal(0, 0).scale + mkDecimal(i0, j0).scale) = mkDecimal(~(i0 * 10 ^ abs(j)), abs(j) + abs(j0))

Rule argument

spec: inst: name: sub-def seq: ⊦ dec_i - dec_j = mkDecimal (dec_i.int * 10 ^ dec_j.scale - dec_j.int * 10 ^ dec_i.scale, dec_i.scale + dec_j.scale) subst: [dec_j, dec_i] → [mkDecimal(i0, j0), mkDecimal(0, 0)] flags: rewrite, current

Additional information

Used terms: mkDecimal(i0, j0), mkDecimal(0, 0)