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Review total electrical resistance for circuit with two resistors in series

abstract:
reference: http://www.dfcd.net/articles/derivations/resistors.html

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4087145886 $V = I R$	no validation is available for declarations
Note about step 2: I is the same across both resistors
2	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	9174439158 $R_1$ 7774819339 $R$ 9830343096 $V_1$ 2698469612 $V$	7675171493 $V_1 = I R_1$	LHS diff is pdg0006599 - pdg0008257 RHS diff is pdg0004501*(pdg0006458 - pdg0008697)
3	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	1484794622 $R_2$ 5890617067 $R$ 1608399874 $V_2$ 7497687256 $V$	6061695358 $V_2 = I R_2$	LHS diff is pdg0006599 - pdg0008721 RHS diff is pdg0004501*(-pdg0003461 + pdg0006458)
Note about step 4: voltage is measured across both resistors
4	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			9063568209 $V_{\rm total} = V_1 + V_2$	no validation is available for declarations
5	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4939880586 $V_{\rm total} = I R_{\rm total}$	no validation is available for declarations
6	0000111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.	9063568209 $V_{\rm total} = V_1 + V_2$ 6061695358 $V_2 = I R_2$ 7675171493 $V_1 = I R_1$ 4939880586 $V_{\rm total} = I R_{\rm total}$		2715678478 $I R_{\rm total} = I R_1 + I R_2$	recognized infrule but not yet supported
7	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2715678478 $I R_{\rm total} = I R_1 + I R_2$	7844317489 $I$	7217021879 $R_{\rm total} = R_1 + R_2$	valid
8	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	7217021879 $R_{\rm total} = R_1 + R_2$			no validation is available for declarations

Symbols used in total electrical resistance for circuit with two resistors in series

0000004501: $ I $
0000006458: $ R $
0000008697: $ R_1 $
0000003461: $ R_2 $
0000001908: $ R_{\rm total} $
0000006599: $ V $
0000008257: $ V_1 $
0000008721: $ V_2 $
0000004691: $ V_{\rm total} $

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timing of Neo4j queries:

0.019 seconds for pdg_app/to_review_derivation a4c86962-3907-4e09-92c5-5648713c39be
0.03 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivatione91c8c5c-73e6-4ee6-997a-a7740f45f039
0.021 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_IDe91c8c5c-73e6-4ee6-997a-a7740f45f039
0.01 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUTe91c8c5c-73e6-4ee6-997a-a7740f45f039
0.006 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEEDe91c8c5c-73e6-4ee6-997a-a7740f45f039
0.008 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUTe91c8c5c-73e6-4ee6-997a-a7740f45f039
0.007 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_stepe91c8c5c-73e6-4ee6-997a-a7740f45f039
0.005 seconds for pdg_app/ a4c86962-3907-4e09-92c5-5648713c39be

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4087145886 \(V = I R\)	no validation is available for declarations
Note about step 2: I is the same across both resistors
2	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	9174439158 \(R_1\) 7774819339 \(R\) 9830343096 \(V_1\) 2698469612 \(V\)	7675171493 \(V_1 = I R_1\)	LHS diff is pdg0006599 - pdg0008257 RHS diff is pdg0004501*(pdg0006458 - pdg0008697)
3	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	1484794622 \(R_2\) 5890617067 \(R\) 1608399874 \(V_2\) 7497687256 \(V\)	6061695358 \(V_2 = I R_2\)	LHS diff is pdg0006599 - pdg0008721 RHS diff is pdg0004501*(-pdg0003461 + pdg0006458)
Note about step 4: voltage is measured across both resistors
4	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			9063568209 \(V_{\rm total} = V_1 + V_2\)	no validation is available for declarations
5	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4939880586 \(V_{\rm total} = I R_{\rm total}\)	no validation is available for declarations
6	0000111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.	9063568209 \(V_{\rm total} = V_1 + V_2\) 6061695358 \(V_2 = I R_2\) 7675171493 \(V_1 = I R_1\) 4939880586 \(V_{\rm total} = I R_{\rm total}\)		2715678478 \(I R_{\rm total} = I R_1 + I R_2\)	recognized infrule but not yet supported
7	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2715678478 \(I R_{\rm total} = I R_1 + I R_2\)	7844317489 \(I\)	7217021879 \(R_{\rm total} = R_1 + R_2\)	valid
8	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	7217021879 \(R_{\rm total} = R_1 + R_2\)			no validation is available for declarations