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Proof step 5 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = gnd ' + gndx0, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ')[n], gndx = [] ∨ gndx.head.start ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], true) = gnd ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gnd ∈ gndx ∨ gnd = mkgnode(nd, n, ndx = [], true) ⊦ gnd.start ∧ (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (gnd ' + gndx0)[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ∧ (¬ # gndx < n1 → (gnd ' + gndx0)[n1].nd = (ndx + nd ')[n1])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = gnd ' + gndx0, gnd = mkgnode(nd0, m, boolvar, boolvar0), ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ')[n], gnd ∈ gndx ∨ gnd = mkgnode(nd, n, ndx = [], true), mkgnode(nd, n, ndx = [], true) = gnd ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gndx = [] ∨ gndx.head.start ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)) ⊦ boolvar ∧ (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (gnd ' + gndx0)[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ∧ (¬ # gndx < n1 → (gnd ' + gndx0)[n1].nd = (ndx + nd ')[n1])

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [gnd, nd0, m, boolvar, boolvar0]

Additional information

Used simplifier rules: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: gnd, nd0, m, boolvar, boolvar0