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Proof step 21 from proof mkDecimal-selectors (previous step)

mkDecimal(i / 10, abs(i0) - 1) = mkDecimal(mkDecimal(i / 10, abs(i0) - 1).int, mkDecimal(i / 10, abs(i0) - 1).scale), i % 10 = 0, ∀ i1, i0. i→n(i1) < i→n(i) → true → mkDecimal(i1, i0) = mkDecimal(mkDecimal(i1, i0).int, mkDecimal(i1, i0).scale) ⊦ i0 = 0, i = 0, mkDecimal(i, i0) = mkDecimal(i / 10, abs(i0) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ dec_i = dec_j ↔ dec_i.int = dec_j.int ∧ dec_i.scale = dec_j.scale
Proof step 23:
mkDecimal(i / 10, abs(i0) - 1) = mkDecimal(mkDecimal(i / 10, abs(i0) - 1).int, mkDecimal(i / 10, abs(i0) - 1).scale), i % 10 = 0, ∀ i1, i0. i→n(i1) < i→n(i) → true → mkDecimal(i1, i0) = mkDecimal(mkDecimal(i1, i0).int, mkDecimal(i1, i0).scale) ⊦ i0 = 0, i = 0, mkDecimal(i, i0).int = mkDecimal(i / 10, abs(i0) - 1).int ∧ mkDecimal(i, i0).scale = mkDecimal(i / 10, abs(i0) - 1).scale

Rule argument

spec: inst: name: Equality seq: ⊦ dec_i = dec_j ↔ dec_i.int = dec_j.int ∧ dec_i.scale = dec_j.scale subst: [dec_j, dec_i] → [mkDecimal(i / 10, abs(i0) - 1), mkDecimal(i, i0)] flags: rewrite, current

Additional information

Used terms: mkDecimal(i / 10, abs(i0) - 1), mkDecimal(i, i0)