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Proof step 83 from proof equality-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) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ j = 0, mkDecimal(0, 0) = mkDecimal(i0, j0) ↔ 0 = i0 * 10 ^ abs(j)

User applied rule insert rewrite lemma

And obtained the following new goals

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(i0, j0), mkDecimal(0, 0)] flags: rewrite, current

Additional information

Used simplifier rules: intvalue-zero: ⊦ mkDecimal(0, j).int = 0;%getint-zero: ⊦ mkDecimal(i, j).int = 0 ↔ i = 0;%scale-zero: ⊦ mkDecimal(0, j).scale = 0;%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%absls: ⊦ ¬ abs(i) < 0; from specification int-abs Used terms: mkDecimal(i0, j0), mkDecimal(0, 0)