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Proof step 5 from proof fill-lastn-04 (previous step)

# fillsgn(m + 1, bits0).rest < m, # bits0 ≤ m ⊦ lastn(m, bits + fillsgn(m + 1, bits0).rest) = fillsgn(m, bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ bits ≠ [] → # bits.rest = (# bits)-1
Proof step 7:
fillsgn(m + 1, bits0) ≠ [], (# fillsgn(m + 1, bits0))-1 < m, # bits0 ≤ m ⊦ lastn(m, bits + fillsgn(m + 1, bits0).rest) = fillsgn(m, bits0)

Rule argument

seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [fillsgn(m + 1, bits0)] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

Used simplifier rules: fill-empty: ⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0;% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: fillsgn(m + 1, bits0)