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Proof step 3 from proof valid-group-nodes-app-transaction (previous step)

transaction(ndx, gndx1) ⊦ valid-group-nodes(gndx0 + gndx1) = (gndx1 = [] ⊃ valid-group-nodes(gndx0);# gndx0 + # gndx1)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 4:
transaction(ndx, gndx1) ⊦ gndx1 = [], valid-group-nodes(gndx0 + gndx1) = # gndx0 + # gndx1

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ gndx + [] = gndx; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]