Choosing the numbering of proposition, assumptions, and corollary, etc

I have the following output

But I would like to have them stated Assumption 1 and Proposition 1 instead. I am using the following in my preamble:

\documentclass[12pt,letterpaper]{article}
\usepackage[margin=1in]{geometry}
\usepackage[english]{babel}
\usepackage{amsmath}
\setcounter{secnumdepth}{3} %the depth of section numbering 0 means no numbering of any section, sub-section and on.
%used for begining theorems and propostions numbered according to the section they are in
\newtheorem{thm}{Theorem}[subsection]% theorem counter resets every \subsection
\renewcommand{\thethm}{\arabic{thm}}% Remove subsection from theorem counter representation
\newtheorem{proposition}[thm]{Proposition}
\newtheorem{assumption}[thm]{Assumption}}


This is basically the part of my test document:

\begin{assumption}
\label{Assumption 1}
\begin{minipage}[t]{.7\linewidth}
\begin{enumerate}
\item[i)]
\item[ii)]
\end{enumerate}
\end{minipage}
\end{assumption}

\begin{proposition}
\label{P1}
Proposition...
\end{proposition}
\noindent {\it Proof}. See Appendix \ref{proofs}. $\blacksquare$


What I would like is it to have the Assumptions numbered by the Assumptions. For example Assumption 2 follows after Assumption 1. And Propositions numbered by Propositions: Proposition 1, Proposition 2, and so on. Similar idea for Corollaries and Lemmas, etc. How do I achieve this?

• By using a common reference counter (here [thm]) you are asking that the same counter be used for all theorem-class objects. What you really want is for each particular type of object to use its own counter, as \newtheorem{proposition}{Proposition}[subsection] \renewcommand{\theproposition}{\arabic{proposition}} and similarly for each type of object. Dec 13 '20 at 23:53

From the above comment, the following in the preamble fixes the problem:

\documentclass[12pt,letterpaper]{article}
\usepackage[margin=1in]{geometry}
\usepackage[english]{babel}
\usepackage{amsmath}
\setcounter{secnumdepth}{3} %the depth of section numbering 0 means no numbering of any section, sub-section and on.
%used for begining theorems and propostions numbered according to the section they are in
\newtheorem{thm}{Theorem}[subsection]% theorem counter resets every \subsection
\renewcommand{\thethm}{\arabic{thm}}% Remove subsection from theorem counter representation
%Numbers the propositions, lemmas, corollaries, etc within themselves
\newtheorem{proposition}{Proposition}[subsection] \renewcommand{\theproposition}{\arabic{proposition}}
\newtheorem{assumption}{Assumption}[subsection]  \renewcommand{\theassumption}{\arabic{assumption}}
\newtheorem{lemma}{Lemma}[subsection]
\renewcommand{\thelemma}{\arabic{lemma}}
\newtheorem{corollary}{Corollary}[subsection] \renewcommand{\thecorollary}{\arabic{corollary}}