Manuscript X-Enter-ST@1 · X-Enter-ST.tex · proposition · f76acc1f

Proposition: Relational combination and matching

Stage E: conditional relational input › The additional classical hypothesis · lines 1080–1105 · proof included or linked

X-Enter-ST@1#prop:matching, X-Enter-ST@1#eq:Irel, X-Enter-ST@1#eq:matching

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Under Assumption ass:reference,

I_{rel} = r_{ε} a - c_{ε} r

is invariant on the witness orbit.

It is invariant under every direction of the specified whole coefficient algebra precisely when

r_{ε} q_{a} (ξ) - c_{ε} q_{r} (ξ) = 0 (ξ \in g_{C}) .

Proof. Substituting the affine witness laws cancels the $λ$ -coefficient in (eq:Irel). For an arbitrary direction $ξ$ , the charge of the same combination is the left side of (eq:matching); its vanishing is exactly the stated first-order invariance.

Displayed formulas in this passage

X-Enter-ST@1#eq:Irel · line 1083
$I_{rel} = r_{ε} a - c_{ε} r$
X-Enter-ST@1#eq:matching · line 1091
$r_{ε} q_{a} (ξ) - c_{ε} q_{r} (ξ) = 0 (ξ \in g_{C}) .$

Proposition: Relational combination and matching

Displayed formulas in this passage

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