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Proof step 21 from proof sis-pos-high (previous step)

# int2bits(j0) = 17, j0 < 65536, 32767 < j0, 0 ≤ j0, 0 < j0 ⊦ j0 = s2i(i2s(bits2int(int2bits(j0).rest))) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1)
Proof step 23:
0 < j0, # int2bits(j0) = 17, j0 < 65536, 32767 < j0, 0 ≤ j0, 0 < j0 ⊦ j0 = s2i(i2s(j0 - 2 ^ (n→i(# uint2bits(j0)) - 1))) + 65536

Rule argument

spec: int2bits inst: name: int2int-rest seq: ⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1) subst: [i] → [j0] flags: rewrite

Additional information

Used terms: j0