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Proof step 10 from proof valid-group-nodes-app-transaction-prefix (previous step)

transaction-prefix(ndx, gndx + mkgnode(nd, m, boolvar, boolvar0) '), ∀ gndx2, ndx, gndx0. # gndx2 < #(gndx + mkgnode(nd, m, boolvar, boolvar0) ') → transaction-prefix(ndx, gndx2) → valid-group-nodes(gndx0 + gndx2) = valid-group-nodes(gndx0) ⊦ (boolvar0 ⊃ (# gndx0 + # gndx) + 1;valid-group-nodes(gndx0 + gndx)) = valid-group-nodes(gndx0)

User applied rule case distinction

And obtained the following new goals

Proof step 11:
¬ boolvar0, transaction-prefix(ndx, gndx + mkgnode(nd, m, boolvar, boolvar0) '), ∀ gndx2, ndx, gndx0. # gndx2 < #(gndx + mkgnode(nd, m, boolvar, boolvar0) ') → transaction-prefix(ndx, gndx2) → valid-group-nodes(gndx0 + gndx2) = valid-group-nodes(gndx0) ⊦ valid-group-nodes(gndx0 + gndx) = valid-group-nodes(gndx0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ¬ transaction-prefix(ndx, gndx + mkgnode(nd, n, boolvar, true) '); (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]