Proof: Do Variables At Unchanged 47

Let's prove the following theorem:

if the following are true:

expression state at time 47 = "begin_expr"
Variables Map at time 47 = [ entry self: (Python reference 0), [ ] ]

then Variables Map at time 48 = [ entry self: (Python reference 0), [ ] ]

Proof:

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Given

1	expression state at time 47 = "begin_expr"
2	Variables Map at time 47 = [ entry self: (Python reference 0), [ ] ]

Proof Table

#	Claim	Reason
1	Variables Map at time (47 + 1) = Variables Map at time 47	if expression state at time 47 = "begin_expr", then Variables Map at time (47 + 1) = Variables Map at time 47 (Insn Count Begin Expression (2))
2	Variables Map at time (47 + 1) = [ entry self: (Python reference 0), [ ] ]	if Variables Map at time (47 + 1) = Variables Map at time 47 and Variables Map at time 47 = [ entry self: (Python reference 0), [ ] ], then Variables Map at time (47 + 1) = [ entry self: (Python reference 0), [ ] ] (Transitive Property of Equality)
3	47 + 1 = 48	47 + 1 = 48 (Fixed Value Statement)
4	Variables Map at time (47 + 1) = Variables Map at time 48	if 47 + 1 = 48, then Variables Map at time (47 + 1) = Variables Map at time 48 (Substitution)
5	Variables Map at time 48 = [ entry self: (Python reference 0), [ ] ]	if Variables Map at time (47 + 1) = Variables Map at time 48 and Variables Map at time (47 + 1) = [ entry self: (Python reference 0), [ ] ], then Variables Map at time 48 = [ entry self: (Python reference 0), [ ] ] (Transitive Property of Equality Variation 2)

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