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Proof step 40 from proof nodes-transaction (previous step)

# lax = # gndx, # ndx = # gndx0 + 1, # lax2 + # lax0 = # gndx0, (mkgnode(nd0, m0, true, boolvar2) ' + gndx0).last = mkgnode(nd1, m1, boolvar1, true), (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), n ∈ gstore, ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[n0].end) ⊦ nd = ndx[# lax2], dups(lax + lax2), dups(lax0), dups(lax2 + lax0), dups((lax + lax2) + lax0), dups(lax), dups(lax2), @(m2, m3) ∈ lax0, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax, n ∈ ginval

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 41:
# ndx = # gndx0 + 1, # lax = # gndx, # lax2 + # lax0 = # gndx0, (mkgnode(nd0, m0, true, boolvar2) ' + gndx0).last = mkgnode(nd1, m1, boolvar1, true), gstore[n] = groupblock(gndx, lax, m), (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), n ∈ gstore, ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[n0].end), ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd0, m0, true, boolvar2) ' + gndx0)[n0].nd = ndx[n0] ⊦ gndx0 = [], nd = ndx[# lax2], dups(lax2), dups(lax), dups((lax + lax2) + lax0), dups(lax2 + lax0), dups(lax0), dups(lax + lax2), n ∈ ginval, @(m2, m3) ∈ lax, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax0

Rule argument

fma: gndx0 = []

Additional information

Used simplifier rules: ⊦ gndx + [] = gndx; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd '.last = gnd; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # lax = 0 ↔ lax = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ gnd '[0] = gnd; (s)% ⊦ mkgnode(nd, m, boolvar, boolvar0).nd = nd; (s)% ⊦ ¬ m < 0; (s)% ⊦ # [] = 0; (s) Used formulas: gndx0 = []