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import Examples.ERC20.Spec
import Solm.Semantics
import Ethereum.Semantics
import Reasoning.JumpDest
/-! # ERC20 — deployed runtime bytecode and trusted-base facts. -/
open Solm Ethereum Ethereum.EVM
/-- `solc --bin-runtime --evm-version shanghai Examples/ERC20/ERC20.sol` (optimizer OFF). -/
def erc20Bytecode : ByteArray :=
⟨#[
96, 128, 96, 64, 82, 52, 128, 21, 97, 0, 15, 87, 95, 95, 253, 91, 80, 96, 4, 54, 16, 97, 0, 96, 87,
95, 53, 96, 224, 28, 128, 99, 9, 94, 167, 179, 20, 97, 0, 100, 87, 128, 99, 24, 22, 13, 221, 20,
97, 0, 148, 87, 128, 99, 35, 184, 114, 221, 20, 97, 0, 178, 87, 128, 99, 112, 160, 130, 49, 20, 97,
0, 226, 87, 128, 99, 169, 5, 156, 187, 20, 97, 1, 18, 87, 128, 99, 221, 98, 237, 62, 20, 97, 1, 66,
87, 91, 95, 95, 253, 91, 97, 0, 126, 96, 4, 128, 54, 3, 129, 1, 144, 97, 0, 121, 145, 144, 97, 7,
153, 86, 91, 97, 1, 114, 86, 91, 96, 64, 81, 97, 0, 139, 145, 144, 97, 7, 241, 86, 91, 96, 64, 81,
128, 145, 3, 144, 243, 91, 97, 0, 156, 97, 2, 95, 86, 91, 96, 64, 81, 97, 0, 169, 145, 144, 97, 8,
25, 86, 91, 96, 64, 81, 128, 145, 3, 144, 243, 91, 97, 0, 204, 96, 4, 128, 54, 3, 129, 1, 144, 97,
0, 199, 145, 144, 97, 8, 50, 86, 91, 97, 2, 101, 86, 91, 96, 64, 81, 97, 0, 217, 145, 144, 97, 7,
241, 86, 91, 96, 64, 81, 128, 145, 3, 144, 243, 91, 97, 0, 252, 96, 4, 128, 54, 3, 129, 1, 144, 97,
0, 247, 145, 144, 97, 8, 130, 86, 91, 97, 5, 65, 86, 91, 96, 64, 81, 97, 1, 9, 145, 144, 97, 8, 25,
86, 91, 96, 64, 81, 128, 145, 3, 144, 243, 91, 97, 1, 44, 96, 4, 128, 54, 3, 129, 1, 144, 97, 1,
39, 145, 144, 97, 7, 153, 86, 91, 97, 5, 85, 86, 91, 96, 64, 81, 97, 1, 57, 145, 144, 97, 7, 241,
86, 91, 96, 64, 81, 128, 145, 3, 144, 243, 91, 97, 1, 92, 96, 4, 128, 54, 3, 129, 1, 144, 97, 1,
87, 145, 144, 97, 8, 173, 86, 91, 97, 6, 232, 86, 91, 96, 64, 81, 97, 1, 105, 145, 144, 97, 8, 25,
86, 91, 96, 64, 81, 128, 145, 3, 144, 243, 91, 95, 129, 96, 1, 95, 51, 115, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129,
82, 96, 32, 1, 144, 129, 82, 96, 32, 1, 95, 32, 95, 133, 115, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1,
144, 129, 82, 96, 32, 1, 95, 32, 129, 144, 85, 80, 130, 115, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 51, 115, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 127, 140, 91,
225, 229, 235, 236, 125, 91, 209, 79, 113, 66, 125, 30, 132, 243, 221, 3, 20, 192, 247, 178, 41,
30, 91, 32, 10, 200, 199, 195, 185, 37, 132, 96, 64, 81, 97, 2, 77, 145, 144, 97, 8, 25, 86, 91,
96, 64, 81, 128, 145, 3, 144, 163, 96, 1, 144, 80, 146, 145, 80, 80, 86, 91, 96, 2, 84, 129, 86,
91, 95, 95, 96, 1, 95, 134, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144, 129, 82, 96, 32, 1, 95,
32, 95, 51, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144, 129, 82, 96, 32, 1, 95, 32, 84, 144, 80,
130, 129, 16, 21, 97, 3, 37, 87, 96, 64, 81, 127, 8, 195, 121, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129, 82, 96, 4, 1, 97, 3, 28, 144, 97, 9, 69,
86, 91, 96, 64, 81, 128, 145, 3, 144, 253, 91, 130, 95, 95, 135, 115, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96,
32, 1, 144, 129, 82, 96, 32, 1, 95, 32, 84, 16, 21, 97, 3, 164, 87, 96, 64, 81, 127, 8, 195, 121,
160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129, 82,
96, 4, 1, 97, 3, 155, 144, 97, 9, 173, 86, 91, 96, 64, 81, 128, 145, 3, 144, 253, 91, 130, 129, 97,
3, 176, 145, 144, 97, 9, 248, 86, 91, 96, 1, 95, 135, 115, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144,
129, 82, 96, 32, 1, 95, 32, 95, 51, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144, 129, 82, 96,
32, 1, 95, 32, 129, 144, 85, 80, 130, 95, 95, 135, 115, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144,
129, 82, 96, 32, 1, 95, 32, 95, 130, 130, 84, 97, 4, 119, 145, 144, 97, 9, 248, 86, 91, 146, 80,
80, 129, 144, 85, 80, 130, 95, 95, 134, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144, 129, 82, 96,
32, 1, 95, 32, 95, 130, 130, 84, 97, 4, 201, 145, 144, 97, 10, 43, 86, 91, 146, 80, 80, 129, 144,
85, 80, 131, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 22, 133, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 22, 127, 221, 242, 82, 173, 27, 226, 200, 155, 105, 194, 176,
104, 252, 55, 141, 170, 149, 43, 167, 241, 99, 196, 161, 22, 40, 245, 90, 77, 245, 35, 179, 239,
133, 96, 64, 81, 97, 5, 45, 145, 144, 97, 8, 25, 86, 91, 96, 64, 81, 128, 145, 3, 144, 163, 96, 1,
145, 80, 80, 147, 146, 80, 80, 80, 86, 91, 95, 96, 32, 82, 128, 95, 82, 96, 64, 95, 32, 95, 145,
80, 144, 80, 84, 129, 86, 91, 95, 129, 95, 95, 51, 115, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129, 82, 96, 32, 1, 144,
129, 82, 96, 32, 1, 95, 32, 84, 16, 21, 97, 5, 213, 87, 96, 64, 81, 127, 8, 195, 121, 160, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129, 82, 96, 4, 1, 97,
5, 204, 144, 97, 9, 173, 86, 91, 96, 64, 81, 128, 145, 3, 144, 253, 91, 129, 95, 95, 51, 115, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22,
115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 22, 129, 82, 96, 32, 1, 144, 129, 82, 96, 32, 1, 95, 32, 95, 130, 130, 84, 97, 6, 32, 145,
144, 97, 9, 248, 86, 91, 146, 80, 80, 129, 144, 85, 80, 129, 95, 95, 133, 115, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 115, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 129,
82, 96, 32, 1, 144, 129, 82, 96, 32, 1, 95, 32, 95, 130, 130, 84, 97, 6, 114, 145, 144, 97, 10, 43,
86, 91, 146, 80, 80, 129, 144, 85, 80, 130, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 51, 115, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 22, 127, 221, 242, 82, 173, 27,
226, 200, 155, 105, 194, 176, 104, 252, 55, 141, 170, 149, 43, 167, 241, 99, 196, 161, 22, 40, 245,
90, 77, 245, 35, 179, 239, 132, 96, 64, 81, 97, 6, 214, 145, 144, 97, 8, 25, 86, 91, 96, 64, 81,
128, 145, 3, 144, 163, 96, 1, 144, 80, 146, 145, 80, 80, 86, 91, 96, 1, 96, 32, 82, 129, 95, 82,
96, 64, 95, 32, 96, 32, 82, 128, 95, 82, 96, 64, 95, 32, 95, 145, 80, 145, 80, 80, 84, 129, 86, 91,
95, 95, 253, 91, 95, 115, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 130, 22, 144, 80, 145, 144, 80, 86, 91, 95, 97, 7, 53, 130, 97, 7,
12, 86, 91, 144, 80, 145, 144, 80, 86, 91, 97, 7, 69, 129, 97, 7, 43, 86, 91, 129, 20, 97, 7, 79,
87, 95, 95, 253, 91, 80, 86, 91, 95, 129, 53, 144, 80, 97, 7, 96, 129, 97, 7, 60, 86, 91, 146, 145,
80, 80, 86, 91, 95, 129, 144, 80, 145, 144, 80, 86, 91, 97, 7, 120, 129, 97, 7, 102, 86, 91, 129,
20, 97, 7, 130, 87, 95, 95, 253, 91, 80, 86, 91, 95, 129, 53, 144, 80, 97, 7, 147, 129, 97, 7, 111,
86, 91, 146, 145, 80, 80, 86, 91, 95, 95, 96, 64, 131, 133, 3, 18, 21, 97, 7, 175, 87, 97, 7, 174,
97, 7, 8, 86, 91, 91, 95, 97, 7, 188, 133, 130, 134, 1, 97, 7, 82, 86, 91, 146, 80, 80, 96, 32, 97,
7, 205, 133, 130, 134, 1, 97, 7, 133, 86, 91, 145, 80, 80, 146, 80, 146, 144, 80, 86, 91, 95, 129,
21, 21, 144, 80, 145, 144, 80, 86, 91, 97, 7, 235, 129, 97, 7, 215, 86, 91, 130, 82, 80, 80, 86,
91, 95, 96, 32, 130, 1, 144, 80, 97, 8, 4, 95, 131, 1, 132, 97, 7, 226, 86, 91, 146, 145, 80, 80,
86, 91, 97, 8, 19, 129, 97, 7, 102, 86, 91, 130, 82, 80, 80, 86, 91, 95, 96, 32, 130, 1, 144, 80,
97, 8, 44, 95, 131, 1, 132, 97, 8, 10, 86, 91, 146, 145, 80, 80, 86, 91, 95, 95, 95, 96, 96, 132,
134, 3, 18, 21, 97, 8, 73, 87, 97, 8, 72, 97, 7, 8, 86, 91, 91, 95, 97, 8, 86, 134, 130, 135, 1,
97, 7, 82, 86, 91, 147, 80, 80, 96, 32, 97, 8, 103, 134, 130, 135, 1, 97, 7, 82, 86, 91, 146, 80,
80, 96, 64, 97, 8, 120, 134, 130, 135, 1, 97, 7, 133, 86, 91, 145, 80, 80, 146, 80, 146, 80, 146,
86, 91, 95, 96, 32, 130, 132, 3, 18, 21, 97, 8, 151, 87, 97, 8, 150, 97, 7, 8, 86, 91, 91, 95, 97,
8, 164, 132, 130, 133, 1, 97, 7, 82, 86, 91, 145, 80, 80, 146, 145, 80, 80, 86, 91, 95, 95, 96, 64,
131, 133, 3, 18, 21, 97, 8, 195, 87, 97, 8, 194, 97, 7, 8, 86, 91, 91, 95, 97, 8, 208, 133, 130,
134, 1, 97, 7, 82, 86, 91, 146, 80, 80, 96, 32, 97, 8, 225, 133, 130, 134, 1, 97, 7, 82, 86, 91,
145, 80, 80, 146, 80, 146, 144, 80, 86, 91, 95, 130, 130, 82, 96, 32, 130, 1, 144, 80, 146, 145,
80, 80, 86, 91, 127, 69, 82, 67, 50, 48, 58, 32, 105, 110, 115, 117, 102, 102, 105, 99, 105, 101,
110, 116, 32, 97, 108, 108, 111, 119, 97, 110, 99, 101, 0, 0, 0, 95, 130, 1, 82, 80, 86, 91, 95,
97, 9, 47, 96, 29, 131, 97, 8, 235, 86, 91, 145, 80, 97, 9, 58, 130, 97, 8, 251, 86, 91, 96, 32,
130, 1, 144, 80, 145, 144, 80, 86, 91, 95, 96, 32, 130, 1, 144, 80, 129, 129, 3, 95, 131, 1, 82,
97, 9, 92, 129, 97, 9, 35, 86, 91, 144, 80, 145, 144, 80, 86, 91, 127, 69, 82, 67, 50, 48, 58, 32,
105, 110, 115, 117, 102, 102, 105, 99, 105, 101, 110, 116, 32, 98, 97, 108, 97, 110, 99, 101, 0, 0,
0, 0, 0, 95, 130, 1, 82, 80, 86, 91, 95, 97, 9, 151, 96, 27, 131, 97, 8, 235, 86, 91, 145, 80, 97,
9, 162, 130, 97, 9, 99, 86, 91, 96, 32, 130, 1, 144, 80, 145, 144, 80, 86, 91, 95, 96, 32, 130, 1,
144, 80, 129, 129, 3, 95, 131, 1, 82, 97, 9, 196, 129, 97, 9, 139, 86, 91, 144, 80, 145, 144, 80,
86, 91, 127, 78, 72, 123, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 95, 82, 96, 17, 96, 4, 82, 96, 36, 95, 253, 91, 95, 97, 10, 2, 130, 97, 7, 102, 86,
91, 145, 80, 97, 10, 13, 131, 97, 7, 102, 86, 91, 146, 80, 130, 130, 3, 144, 80, 129, 129, 17, 21,
97, 10, 37, 87, 97, 10, 36, 97, 9, 203, 86, 91, 91, 146, 145, 80, 80, 86, 91, 95, 97, 10, 53, 130,
97, 7, 102, 86, 91, 145, 80, 97, 10, 64, 131, 97, 7, 102, 86, 91, 146, 80, 130, 130, 1, 144, 80,
128, 130, 17, 21, 97, 10, 88, 87, 97, 10, 87, 97, 9, 203, 86, 91, 91, 146, 145, 80, 80, 86, 254,
162, 100, 105, 112, 102, 115, 88, 34, 18, 32, 161, 128, 50, 41, 20, 78, 209, 13, 48, 81, 98, 5, 60,
170, 48, 113, 117, 235, 74, 39, 180, 167, 49, 5, 220, 216, 169, 41, 169, 39, 1, 209, 100, 115, 111,
108, 99, 67, 0, 8, 35, 0, 51
]⟩
/-! ## Constructor/initcode bytecode
For constructor-equivalence we use compact straight-line initcode, following `CtorStore` and
`SimpleAuction`: it enforces the nonpayable constructor guard, copies the appended ABI
`initialSupply` word, writes `balanceOf[msg.sender]`, writes `totalSupply`, and returns the deployed
runtime above.
-/
/-- Constructor prefix; the deployed runtime starts at byte offset 55. -/
def erc20CtorPrefix : ByteArray :=
⟨#[
0x34, -- CALLVALUE
0x80, -- DUP1
0x15, -- ISZERO
0x60, 0x09, -- PUSH1 0x09 ; nonpayable-ok target
0x57, -- JUMPI
0x5f, -- PUSH0
0x5f, -- PUSH0
0xfd, -- REVERT
0x5b, -- JUMPDEST
0x50, -- POP
0x60, 0x80, -- PUSH1 0x80
0x60, 0x40, -- PUSH1 0x40
0x52, -- MSTORE ; free-memory pointer word
0x60, 0x20, -- PUSH1 0x20 ; one ABI word
0x61, 0x0a, 0xcb, -- PUSH2 0x0acb ; initialSupply ABI word
0x60, 0x40, -- PUSH1 0x40 ; memory dst
0x39, -- CODECOPY
0x60, 0x40, -- PUSH1 0x40
0x51, -- MLOAD ; initialSupply
0x80, -- DUP1 ; keep a copy for totalSupply
0x33, -- CALLER
0x5f, -- PUSH0
0x52, -- MSTORE ; mapping key
0x5f, -- PUSH0 ; mapping base slot 0
0x60, 0x20, -- PUSH1 0x20
0x52, -- MSTORE
0x60, 0x40, -- PUSH1 0x40
0x5f, -- PUSH0
0x20, -- KECCAK256 ; balanceOf[msg.sender] slot
0x55, -- SSTORE
0x60, 0x02, -- PUSH1 0x02 ; totalSupply slot
0x55, -- SSTORE
0x61, 0x0a, 0x94, -- PUSH2 0x0a94 ; runtime length
0x60, 0x37, -- PUSH1 0x37 ; runtime offset
0x5f, -- PUSH0
0x39, -- CODECOPY
0x61, 0x0a, 0x94, -- PUSH2 0x0a94
0x5f, -- PUSH0
0xf3 -- RETURN
]⟩
/-- Pure creation/initcode for `ERC20`, without appended constructor ABI arguments. -/
def erc20Initcode : ByteArray := erc20CtorPrefix ++ erc20Bytecode
/-- `keccak("approve(address,uint256)")[0:4] = 0x095ea7b3`. -/
axiom erc20ApproveSelectorBytes :
(ffi.KEC (String.toByteArray (Solm.transitionSigStr ERC20.approveTransition))).extract 0 4
= ⟨#[0x09, 0x5e, 0xa7, 0xb3]⟩
/-- `keccak("totalSupply()")[0:4] = 0x18160ddd`. -/
axiom erc20TotalSupplySelectorBytes :
(ffi.KEC (String.toByteArray (Solm.transitionSigStr ERC20.totalSupplyTransition))).extract 0 4
= ⟨#[0x18, 0x16, 0x0d, 0xdd]⟩
/-- `keccak("transferFrom(address,address,uint256)")[0:4] = 0x23b872dd`. -/
axiom erc20TransferFromSelectorBytes :
(ffi.KEC (String.toByteArray (Solm.transitionSigStr ERC20.transferFromTransition))).extract 0 4
= ⟨#[0x23, 0xb8, 0x72, 0xdd]⟩
/-- `keccak("balanceOf(address)")[0:4] = 0x70a08231`. -/
axiom erc20BalanceOfSelectorBytes :
(ffi.KEC (String.toByteArray (Solm.transitionSigStr ERC20.balanceOfTransition))).extract 0 4
= ⟨#[0x70, 0xa0, 0x82, 0x31]⟩
/-- `keccak("transfer(address,uint256)")[0:4] = 0xa9059cbb`. -/
axiom erc20TransferSelectorBytes :
(ffi.KEC (String.toByteArray (Solm.transitionSigStr ERC20.transferTransition))).extract 0 4
= ⟨#[0xa9, 0x05, 0x9c, 0xbb]⟩
/-- `keccak("allowance(address,address)")[0:4] = 0xdd62ed3e`. -/
axiom erc20AllowanceSelectorBytes :
(ffi.KEC (String.toByteArray (Solm.transitionSigStr ERC20.allowanceTransition))).extract 0 4
= ⟨#[0xdd, 0x62, 0xed, 0x3e]⟩
/-- The `JUMPDEST` set of `erc20Bytecode` (computed with PUSH-data skipping). -/
@[valid_jumps] theorem erc20ValidJumps :
Ethereum.EVM.D_J erc20Bytecode 0
= #[⟨15⟩, ⟨96⟩, ⟨100⟩, ⟨121⟩, ⟨126⟩, ⟨139⟩, ⟨148⟩, ⟨156⟩, ⟨169⟩, ⟨178⟩, ⟨199⟩,
⟨204⟩, ⟨217⟩, ⟨226⟩, ⟨247⟩, ⟨252⟩, ⟨265⟩, ⟨274⟩, ⟨295⟩, ⟨300⟩, ⟨313⟩, ⟨322⟩,
⟨343⟩, ⟨348⟩, ⟨361⟩, ⟨370⟩, ⟨589⟩, ⟨607⟩, ⟨613⟩, ⟨796⟩, ⟨805⟩, ⟨923⟩, ⟨932⟩,
⟨944⟩, ⟨1143⟩, ⟨1225⟩, ⟨1325⟩, ⟨1345⟩, ⟨1365⟩, ⟨1484⟩, ⟨1493⟩, ⟨1568⟩, ⟨1650⟩,
⟨1750⟩, ⟨1768⟩, ⟨1800⟩, ⟨1804⟩, ⟨1835⟩, ⟨1845⟩, ⟨1852⟩, ⟨1861⟩, ⟨1871⟩, ⟨1874⟩,
⟨1888⟩, ⟨1894⟩, ⟨1903⟩, ⟨1912⟩, ⟨1922⟩, ⟨1925⟩, ⟨1939⟩, ⟨1945⟩, ⟨1966⟩, ⟨1967⟩,
⟨1980⟩, ⟨1997⟩, ⟨2007⟩, ⟨2018⟩, ⟨2027⟩, ⟨2033⟩, ⟨2052⟩, ⟨2058⟩, ⟨2067⟩, ⟨2073⟩,
⟨2092⟩, ⟨2098⟩, ⟨2120⟩, ⟨2121⟩, ⟨2134⟩, ⟨2151⟩, ⟨2168⟩, ⟨2178⟩, ⟨2198⟩, ⟨2199⟩,
⟨2212⟩, ⟨2221⟩, ⟨2242⟩, ⟨2243⟩, ⟨2256⟩, ⟨2273⟩, ⟨2283⟩, ⟨2299⟩, ⟨2339⟩, ⟨2351⟩,
⟨2362⟩, ⟨2373⟩, ⟨2396⟩, ⟨2403⟩, ⟨2443⟩, ⟨2455⟩, ⟨2466⟩, ⟨2477⟩, ⟨2500⟩, ⟨2507⟩,
⟨2552⟩, ⟨2562⟩, ⟨2573⟩, ⟨2596⟩, ⟨2597⟩, ⟨2603⟩, ⟨2613⟩, ⟨2624⟩, ⟨2647⟩, ⟨2648⟩]
:= by native_decide