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Proof step 11 from proof fix-butlast-longer (previous step)

# bytes < n ⊦ bytes = [], # bytes = 1, fillsgn(n + 1, bytes).butlast = fillsgn(n, bytes).first ' + fillsgn(n, bytes).butlast

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
fillsgn(n, bytes) = by + bytes0 ∧ fillsgn(n, bytes) ≠ [], # bytes < n ⊦ bytes = [], # bytes = 1, fillsgn(n + 1, bytes).butlast = by ' + fillsgn(n, bytes).butlast

Rule argument

seq: bytes ≠ [] ⊦ by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0 subst: [bytes, by, bytes0] → [fillsgn(n, bytes), by, bytes0] rotate: T spec: list-data inst: bytelist name: elim-list-c

Additional information

Used simplifier rules: fillsgn-empty: ⊦ fillsgn(n, bytes) = [] ↔ n = 0 ∧ bytes = [];% ⊦ m < n → n ≠ 0;%bytes ≠ [] ⊦ by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0; (elim) Used terms: fillsgn(n, bytes), by, bytes0