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Proof step 12 from proof valid-group-nodes-app-transaction-prefix (previous step)

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

User applied rule apply induction

And closed the goal!

Rule argument

subst: [gndx2, ndx, gndx0] → [gndx, ndx, gndx0]

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%⊦ transaction-prefix(ndx, gndx0 + gndx1) → transaction-prefix(ndx, gndx0); (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ # gnd ' = 0 +1; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: gndx, ndx, gndx0