Proof: Write Stmt Expr State At Unchanged 12

Let's prove the following theorem:

if the following are true:

the line at time 12 = 3
the tab at time 12 = 0
statement at line 3, tab 0 = else:
expression state at time 12 = "not_expr"

then expression state at time 13 = "not_expr"

Proof:

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Given

1	the line at time 12 = 3
2	the tab at time 12 = 0
3	statement at line 3, tab 0 = `else:`
4	expression state at time 12 = "not_expr"

Proof Table

#	Claim	Reason
1	expression state at time (12 + 1) = expression state at time 12	if the line at time 12 = 3 and the tab at time 12 = 0 and statement at line 3, tab 0 = `else:`, then expression state at time (12 + 1) = expression state at time 12 (Else Unchanged (8))
2	expression state at time (12 + 1) = "not_expr"	if expression state at time (12 + 1) = expression state at time 12 and expression state at time 12 = "not_expr", then expression state at time (12 + 1) = "not_expr" (Transitive Property of Equality)
3	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
4	expression state at time (12 + 1) = expression state at time 13	if 12 + 1 = 13, then expression state at time (12 + 1) = expression state at time 13 (Substitution)
5	expression state at time 13 = "not_expr"	if expression state at time (12 + 1) = expression state at time 13 and expression state at time (12 + 1) = "not_expr", then expression state at time 13 = "not_expr" (Transitive Property of Equality Variation 2)

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