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Proof step 35 from proof sis-pos-high (previous step)

# int2bits(j0) = 17, 0 < i0, j0 < 65536, 32767 < i0 * 65536 + j0, 32767 < j0, 0 ≤ j0, 0 ≤ i0, 0 < i0 * 65536 + j0, 0 < j0 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j0)).rest)))) + 65536, fillsgn(17, int2bits(j0)) = [], 16 = # fillsgn(17, int2bits(j0)) - 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: bitopsaux inst: name: fill-length seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [int2bits(j0), 17] flags: rewrite

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%commutativity: ⊦ i * j = j * i; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: int2bits(j0), 17