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Proof step 18 from proof sis-pos-high (previous step)

# int2bits(j0) = 17, j0 < 65536, 32767 < j0, 0 ≤ j0, 0 < j0 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(j0))))) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ # bits = n + 1 → lastn(n, bits) = bits.rest
Proof step 20:
# int2bits(j0) = 16 + 1, # int2bits(j0) = 17, j0 < 65536, 32767 < j0, 0 ≤ j0, 0 < j0 ⊦ j0 = s2i(i2s(bits2int(int2bits(j0).rest))) + 65536

Rule argument

spec: list-del inst: bitlista name: lastN-rest-01 seq: ⊦ # bits = n + 1 → lastn(n, bits) = bits.rest subst: [bits, n] → [int2bits(j0), 16] flags: rewrite

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: int2bits(j0), 16