'arith.muli' op requires the same type for all operands and results

Here is a minimal reproducible code:

#include <stdint.h>

void foo(uint16_t *a, uint16_t len) {
    uint16_t c = 1;
    for (uint16_t i = 0; i < len; i++) {
        c *= a[i];
        a[i] = c;
    }
}

  "func.func"() ({
  ^bb0(%arg0: memref<?xi16>, %arg1: i16):
    %0 = "arith.constant"() {value = 0 : index} : () -> index
    %1 = "arith.constant"() {value = 1 : index} : () -> index
    %2 = "arith.constant"() {value = 1 : i16} : () -> i16
    %3 = "arith.index_cast"(%arg1) : (i16) -> index
    %4 = "scf.for"(%0, %3, %1, %2) ({
    ^bb0(%arg2: index, %arg3: i16):
      %5 = "memref.load"(%arg0, %arg2) : (memref<?xi16>, index) -> i16
      %6 = "arith.extsi"(%5) : (i16) -> i32
      %7 = "arith.muli"(%arg3, %6) : (i16, i32) -> i16
      "memref.store"(%7, %arg0, %arg2) : (i16, memref<?xi16>, index) -> ()
      "scf.yield"(%7) : (i16) -> ()
    }) : (index, index, index, i16) -> i16
    "func.return"() : () -> ()
  }) {function_type = (memref<?xi16>, i16) -> (), llvm.linkage = #llvm.linkage<external>, sym_name = "foo"} : () -> ()

arith.extsi is unnecessary and actually triggers the error.

Start with the minimal C reproducer and its generated MLIR, focusing on the arith.extsi and arith.muli operations inside the scf.for body. Trace why the unnecessary extension produces mixed operand and result types, then verify that the reproducer no longer emits the invalid arith.muli operation.