theorem
proved
term proof
plot_composition_xor_additive
show as:
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formal statement (Lean)
217theorem plot_composition_xor_additive (p q : BookerPlotFamily)
218 (h : plotEncoding p + plotEncoding q ≠ 0) :
219 ∃ r : BookerPlotFamily,
220 plotEncoding r = plotEncoding p + plotEncoding q :=
proof body
Term-mode proof.
221 no_eighth_plot _ h
222
223/-- The companion to Falsifier 3: when the composite XOR is zero
224 (the two plots cancel), the composite is the trivial transition,
225 i.e., `p = q` (since `v + v = 0` in characteristic 2 and the
226 encoding is injective). -/