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Proof step 18 from proof inv-transaction (previous step)

# gndx = # ndx3, transaction-prefix(ndx3 + nd ' + ndx0, gndx) ⊦ (ndx0 = [] → transaction(ndx3 + nd ', gndx + mkgnode(nd, jmaxino0 + # ndx3, ndx3 = [], true) ')) ∧ (ndx0 ≠ [] → transaction-prefix(ndx3 + nd ' + ndx0, gndx + mkgnode(nd, jmaxino0 + # ndx3, ndx3 = [], false) '))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
ndx1 ≠ [], # ndx = # gndx ⊦ transaction-prefix(ndx + nd ' + ndx1, gndx) → transaction-prefix(ndx + nd ' + ndx1, gndx + mkgnode(nd, n, ndx = [], false) ')
Proof step 20:
# gndx = # ndx3, transaction-prefix(ndx3 + nd ' + ndx0, gndx) ⊦ (ndx0 = [] → transaction(ndx3 + nd ', gndx + mkgnode(nd, jmaxino0 + # ndx3, ndx3 = [], true) ')) ∧ (ndx0 ≠ [] → transaction-prefix(ndx3 + nd ' + ndx0, gndx + mkgnode(nd, jmaxino0 + # ndx3, ndx3 = [], false) ')), ndx0 ≠ [] ∧ # ndx3 = # gndx ∧ transaction-prefix(ndx3 + nd ' + ndx0, gndx)

Rule argument

spec: gjournal-base name: transaction-prefix-app-nonlast seq: ndx1 ≠ [], # ndx = # gndx ⊦ transaction-prefix(ndx + nd ' + ndx1, gndx) → transaction-prefix (ndx + nd ' + ndx1, gndx + mkgnode(nd, n, ndx = [], false) ') subst: [n, gndx, ndx1, nd, ndx] → [jmaxino0 + # ndx3, gndx, ndx0, nd, ndx3] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list] Used terms: jmaxino0 + # ndx3, gndx, ndx0, nd, ndx3