Proof: Do Expr At Unchanged 1

Let's prove the following theorem:

if the following are true:

expression state at time 1 = "begin_expr"
the expression at time 1 = __eq__(1, 3)

then the expression at time 2 = __eq__(1, 3)

Proof:

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Given

1	expression state at time 1 = "begin_expr"
2	the expression at time 1 = `__eq__(1, 3)`

Proof Table

#	Claim	Reason
1	the expression at time (1 + 1) = the expression at time 1	if expression state at time 1 = "begin_expr", then the expression at time (1 + 1) = the expression at time 1 (Insn Count Begin Expression (1))
2	the expression at time (1 + 1) = `__eq__(1, 3)`	if the expression at time (1 + 1) = the expression at time 1 and the expression at time 1 = `__eq__(1, 3)`, then the expression at time (1 + 1) = `__eq__(1, 3)` (Transitive Property of Equality)
3	1 + 1 = 2	1 + 1 = 2 (Fixed Value Statement)
4	the expression at time (1 + 1) = the expression at time 2	if 1 + 1 = 2, then the expression at time (1 + 1) = the expression at time 2 (Substitution)
5	the expression at time 2 = `__eq__(1, 3)`	if the expression at time (1 + 1) = the expression at time 2 and the expression at time (1 + 1) = `__eq__(1, 3)`, then the expression at time 2 = `__eq__(1, 3)` (Transitive Property of Equality Variation 2)

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