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Proof step 5 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) ⊦ gndx1 = [], valid-group-nodes(gndx0 + gndx1) = valid-group-nodes(gndx0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ gndx = [] ↔ ¬(∃ gndx0, gnd. gndx = gndx0 + gnd ')
Proof step 7:
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), ∀ gndx0, gnd. gndx1 ≠ gndx0 + gnd '

Rule argument

spec: list, inst: group-store name: lastdiv-rew seq: ⊦ gndx = [] ↔ ¬(∃ gndx0, gnd. gndx = gndx0 + gnd ') subst: [gndx] → [gndx1] flags: <all paths>

Additional information

Used terms: gndx1