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Proof step 33 from proof sis-neg-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-data inst: bitlista name: length-rest seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [int2bits(j0)] flags: rewrite

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat%int2bits-not-empty: ⊦ int2bits(j) ≠ []; from specification int2bits%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%ls: n0 ≤ n ⊦ m < n - n0 ↔ m + n0 < n; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%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 Used terms: int2bits(j0)