Proof: Do Variables At Unchanged 11

Let's prove the following theorem:

if the following are true:

expression state at time 11 = "begin_expr"
Variables Map at time 11 = [ ]

then Variables Map at time 12 = [ ]

Proof:

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Given

1	expression state at time 11 = "begin_expr"
2	Variables Map at time 11 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (11 + 1) = Variables Map at time 11	if expression state at time 11 = "begin_expr", then Variables Map at time (11 + 1) = Variables Map at time 11 (Insn Count Begin Expression (2))
2	Variables Map at time (11 + 1) = [ ]	if Variables Map at time (11 + 1) = Variables Map at time 11 and Variables Map at time 11 = [ ], then Variables Map at time (11 + 1) = [ ] (Transitive Property of Equality)
3	11 + 1 = 12	11 + 1 = 12 (Fixed Value Statement)
4	Variables Map at time (11 + 1) = Variables Map at time 12	if 11 + 1 = 12, then Variables Map at time (11 + 1) = Variables Map at time 12 (Substitution)
5	Variables Map at time 12 = [ ]	if Variables Map at time (11 + 1) = Variables Map at time 12 and Variables Map at time (11 + 1) = [ ], then Variables Map at time 12 = [ ] (Transitive Property of Equality Variation 2)

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