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Proof step 2 from proof short-succ (previous step)

s2i(sho) < 32767 ⊦ s2i(i2s(s2i(sho) + 1)) = s2i(sho) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: num-issi rotate: F subst: [i] → [s2i(sho) + 1]

Additional information

Used simplifier rules: short-min-02: ⊦ i ≤ ~32768 → ¬ s2i(sho) < i;%short-32767: ⊦ 32766 < s2i(sho) ↔ s2i(sho) = 32767;%sis-pos-upper: ⊦ 32768 ≤ i ∧ i < 65536 → s2i(i2s(i)) = i - 65536;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) Used terms: s2i(sho) + 1