def AP.index_of_nat.go

bend-osdev-array@0.1.0.1 · PROOF.bend:1319

import Base
import bend-osdev-array@0.1.0.1/array.bend as A

1319def AP.index_of_nat.go(+d: Nat, +hd: {Nat.is_lt(d, 32n) == True{} : Bool}, +k: Nat, +hk: {Nat.is_lt(k, A.Arrays.slots(d)) == True{} : Bool}) -> {A.Arrays.index(d, U32.from_nat(k)) == k : Nat}:
1320  +a = U32.from_nat(k)
1321  +fk = AP.from_nat(k, d, hk, AP.lt_le(d, 32n, hd))
1322  %Equal.sym(U32, U32.sub(U32.shln(1, d), 1), U32{AP.lm(32n, d)}, AP.mask_lm(d)) : {U32.to_nat(U32.and(a, _)) == k : Nat}
1323  %Equal.sym(U32, U32.and(a, U32{AP.lm(32n, d)}), a, AP.u32_and_id(a, d, AP.lt_rw_l(U32.to_nat(a), k, A.Arrays.slots(d), fk, hk))) : {U32.to_nat(_) == k : Nat}
1324  fk