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Proof step 24 from proof int2bits-leneq-neg (previous step)

# int2bits(j) = i→n(i0 + 2), j < ~1, j < 0, i→n(i0 + 2) ≤ i→n(i0) + 1, 0 < i0 ⊦ i0 = 1, ~2 = i0, 0 = i0, ~1 = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intnat inst: name: add-01 seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j) subst: [j, i] → [2, i0] flags: rewrite

Additional information

Used simplifier rules: ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%le-num-02: n0 < n ⊦ m + (* n) ≤ m0 + (* n0) ↔ m + (n - n0) ≤ m0; from specification nat%le-add: ⊦ m + m0 ≤ m ↔ m0 = 0; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: 2, i0