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Proof step 4 from proof valid-group-nodes-app-transaction-prefix (previous step)

transaction-prefix(ndx, gndx1), ∀ gndx, ndx, gndx0. # gndx < # gndx1 → transaction-prefix(ndx, gndx) → valid-group-nodes(gndx0 + gndx) = valid-group-nodes(gndx0) ⊦ valid-group-nodes(gndx0 + gndx1) = valid-group-nodes(gndx0)

User applied rule cut formula

And obtained the following new goals

Proof step 5:
transaction-prefix(ndx, gndx1), ∀ gndx, ndx, gndx0. # gndx < # gndx1 → transaction-prefix(ndx, gndx) → valid-group-nodes(gndx0 + gndx) = valid-group-nodes(gndx0) ⊦ gndx1 = [], valid-group-nodes(gndx0 + gndx1) = valid-group-nodes(gndx0)

Rule argument

fma: gndx1 = []

Additional information

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