def un.shl_w

bend-osdev-u32@0.1.0.0 · PROOF.bend:766

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U

766def un.shl_w(n: Nat, w: Word(n), h: {Nat.is_lt(Nat.double(Word.to_nat(n, w)), U.U32Nat.dbl(n, 1n)) == True{} : Bool}) -> {Word.to_nat(n, Word.shl(n, w)) == Nat.double(Word.to_nat(n, w)) : Nat}:
767  match n:
768    case 0n:
769      match w:
770        case WNil{}:
771          {==}
772    case 1n+ +p:
773      match w:
774        case WCon{False{}, +t}:
775          +k = U.U32Nat.dbl(p, 1n)
776          +x = Word.to_nat(p, t)
777          un.double_cong(Word.to_nat(p, Word.shl.put(p, False{}, t)), Nat.double(x), un.shlput(p, False{}, t, Equal.trans(Bool, Nat.is_lt(Nat.double(x), k), Nat.is_lt(Nat.double(Nat.double(x)), Nat.double(k)), True{}, Equal.sym(Bool, Nat.is_lt(Nat.double(Nat.double(x)), Nat.double(k)), Nat.is_lt(Nat.double(x), k), un.lt_dbl(Nat.double(x), k)), h)))
778        case WCon{True{}, +t}:
779          +k = U.U32Nat.dbl(p, 1n)
780          +x = Word.to_nat(p, t)
781          un.double_cong(Word.to_nat(p, Word.shl.put(p, True{}, t)), 1n+Nat.double(x), un.shlput(p, True{}, t, Equal.trans(Bool, Nat.is_lt(1n+Nat.double(x), k), Nat.is_lt(Nat.double(1n+Nat.double(x)), Nat.double(k)), True{}, Equal.sym(Bool, Nat.is_lt(Nat.double(1n+Nat.double(x)), Nat.double(k)), Nat.is_lt(1n+Nat.double(x), k), un.lt_dbl(1n+Nat.double(x), k)), h)))