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Proof step 11 from proof ushort-pos-01 (previous step)

s2i(i2s(i)) < 0, 0 ≤ i, i < 65536 ⊦ s2i(i2s(i)) + 65536 = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i
Proof step 13:
¬(~32768 ≤ i ∧ i ≤ 32767), s2i(i2s(i)) < 0, 0 ≤ i, i < 65536 ⊦ s2i(i2s(i)) + 65536 = i

Rule argument

name: num-issi rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: ⊦ i = i + j ↔ j = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i