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Proof step 36 from proof sis-neg-low (previous step)

# int2bits(j0) = 17, 16 = # int2bits(j0).rest, j0 < 0, j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 * 65536 + j0 < 0, i0 < 0 ⊦ int2bits(j0).rest = [], j0 = 0, s2i(i2s(bits2int(int2bits(j0).rest))) = j0 + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ j < ~1 → bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1)
Proof step 38:
j0 < ~1, # int2bits(j0) = 17, 16 = # int2bits(j0).rest, j0 < 0, j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 * 65536 + j0 < 0, i0 < 0 ⊦ int2bits(j0).rest = [], j0 = 0, s2i(i2s(j0 + 2 ^ (n→i(# int2bits(j0)) - 1))) = j0 + 65536

Rule argument

spec: int2bits inst: name: int2int-rest-01 seq: ⊦ j < ~1 → bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1) subst: [j] → [j0] flags: rewrite

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%numlslsdel: j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0); from specification int-basic1 Used terms: j0