def cnt_pw

bendtorch@1.3.0.0 · PROOF.bend:212

import Base
import bendtorch@1.3.0.0/main.bend as T
import bend-ml-nat-lemmas@0.1.2.0/main.bend as NL

212# pw writes xs and counts them from n; the softmax prow3 runs on them reports 1 + (|xs| + n - 1)
213def cnt_pw(+xs: List<&2, F32>, +idx: U32, +sc: F32, +n: Nat, +off: U32, q: Array<F32>, k: Array<F32>, p: Array<F32>) -> {T.pr_n(T.prow3(off, q, k, T.pw(xs, idx, sc, n, p))) == 1n+Nat.sub(Nat.add(List.length(&2, F32, xs), n), 1n) : Nat}:
214  match xs:
215    case Nil{}:
216      cnt_psm2(q, k, Nat.sub(n, 1n), off, T.pmax0(Nat.sub(n, 1n), off, Array.get(F32, p, off)))
217    case Con{+x, +t}:
218      Equal.trans(Nat, T.pr_n(T.prow3(off, q, k, T.pw(t, (idx + 1 : U32), sc, 1n+n, Array.set(F32, p, idx, (x * sc : F32))))), 1n+Nat.sub(Nat.add(List.length(&2, F32, t), 1n+n), 1n), 1n+Nat.sub(1n+Nat.add(List.length(&2, F32, t), n), 1n), cnt_pw(t, (idx + 1 : U32), sc, 1n+n, off, q, k, Array.set(F32, p, idx, (x * sc : F32))), Equal.cong(Nat, Nat, z => 1n+Nat.sub(z, 1n), Nat.add(List.length(&2, F32, t), 1n+n), 1n+Nat.add(List.length(&2, F32, t), n), Equal.sym(Nat, 1n+Nat.add(List.length(&2, F32, t), n), Nat.add(List.length(&2, F32, t), 1n+n), NL.add_succ(List.length(&2, F32, t), n))))