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Proof step 2 from proof add-scale-neq (previous step)

⊦ dec_i.scale = dec_j.scale, (dec_i + dec_j).scale = max(dec_i.scale, dec_j.scale)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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 4:
⊦ dec_i.scale = dec_j.scale, mkDecimal(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale, dec_i.scale + dec_j.scale).scale = max(dec_i.scale, dec_j.scale)

Rule argument

spec: inst: name: add-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] → [dec_j, dec_i] flags: rewrite, current

Additional information

Used terms: dec_j, dec_i