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Proof step 11 from proof fits-law-add (previous step)

32768 ≤ b2i(by1) + b2i(by2), 0 < b2i(by1) + b2i(by2), 0 ≤ b2i(by1) + b2i(by2) ⊦ 32768 ≤ b2i(by1) + 127, b2i(by1) + b2i(by2) = s2i(i2s(b2i(by1) + b2i(by2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i0 ≤ i + j ∧ j ≤ j0 → i0 ≤ i + j0 subst: [i0, i, j, j0] → [32768, b2i(by1), b2i(by2), 127] rotate: F spec: int-abs inst: name: estimate-add2-le-right

Additional information

Used simplifier rules: byte-nge: i ≥ 128 ⊦ ¬ (* i) ≤ b2i(by);%byte-le: ⊦ b2i(by) ≤ 127;% ⊦ i + j = j + i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 32768, b2i(by1), b2i(by2), 127