Proof: Do Variables At Unchanged 36

Let's prove the following theorem:

if the following are true:

expression state at time 36 = "begin_expr"
Variables Map at time 36 = [ entry locations: (Python reference 0), [ ] ]

then Variables Map at time 37 = [ entry locations: (Python reference 0), [ ] ]

Proof:

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Given

1	expression state at time 36 = "begin_expr"
2	Variables Map at time 36 = [ entry locations: (Python reference 0), [ ] ]

Proof Table

#	Claim	Reason
1	Variables Map at time (36 + 1) = Variables Map at time 36	if expression state at time 36 = "begin_expr", then Variables Map at time (36 + 1) = Variables Map at time 36 (Insn Count Begin Expression (2))
2	Variables Map at time (36 + 1) = [ entry locations: (Python reference 0), [ ] ]	if Variables Map at time (36 + 1) = Variables Map at time 36 and Variables Map at time 36 = [ entry locations: (Python reference 0), [ ] ], then Variables Map at time (36 + 1) = [ entry locations: (Python reference 0), [ ] ] (Transitive Property of Equality)
3	36 + 1 = 37	36 + 1 = 37 (Fixed Value Statement)
4	Variables Map at time (36 + 1) = Variables Map at time 37	if 36 + 1 = 37, then Variables Map at time (36 + 1) = Variables Map at time 37 (Substitution)
5	Variables Map at time 37 = [ entry locations: (Python reference 0), [ ] ]	if Variables Map at time (36 + 1) = Variables Map at time 37 and Variables Map at time (36 + 1) = [ entry locations: (Python reference 0), [ ] ], then Variables Map at time 37 = [ entry locations: (Python reference 0), [ ] ] (Transitive Property of Equality Variation 2)

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