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Proof step 18 from proof sis-neg-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ j < ~1 → bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1)
Proof step 20:
j0 < ~1, # int2bits(j0) = 17, ~65536 < j0, j0 < ~32768, j0 < 0 ⊦ 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: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%mone-08: ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); from specification int-abs%int2bits-mone-02: ⊦ int2bits(~1) = true '; from specification int2bits%len-02: ⊦ # boolvar ' = 0 +1; from specification list[bitlista] Used terms: j0