def shl_value

bend-collections-laws-math@1.0.0.0 · proofs/lib/u32.bend:118

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

118def shl_value(+x: U32, +k: Nat, +hk: {Nat.is_le(k, 32n) == True{} : Bool}, +h: {Nat.is_lt(Nat.double(U32.to_nat(x)), SC.pow2(k)) == True{} : Bool}) -> {U32.to_nat(U32.shl(x)) == Nat.double(U32.to_nat(x)) : Nat}:
119  match x:
120    case U32{+w}:
121      %Equal.sym(Nat, U32.to_nat(U32{w}), S.unsigned(32n, w), to_nat_word(w)) : {U32.to_nat(U32{Word.shl(32n, w)}) == Nat.double(_) : Nat}
122      Equal.trans(Nat, U32.to_nat(U32{Word.shl(32n, w)}), S.unsigned(32n, Word.shl(32n, w)), Nat.double(S.unsigned(32n, w)), to_nat_word(Word.shl(32n, w)),
123        shl_exact_k(32n, k, w, hk, shl_bound(w, k, h)))