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Proof step 35 from proof nodes-transaction (previous step)

# ndx = # gndx1, # lax = # gndx, # lax2 + # lax0 + 1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gndx1 = gnd + gndx0, gndx1.last.end, gnd.start, n ∈ gstore, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx1 → ¬ gndx1[n0].start) ∧ (n0 + 1 < # gndx1 → ¬ gndx1[n0].end), ∀ n. n < # gndx1 → gndx1[n].nd = ndx[n] ⊦ gndx1 = [], 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# lax = # gndx, # ndx = # gndx0 + 1, # lax2 + # lax0 = # gndx0, (gnd ' + gndx0)[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), (gnd ' + gndx0).last.end, gnd.start, n ∈ gstore, ∀ n0. ¬ # gndx0 < n0 → (gnd ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (gnd ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (gnd ' + 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

Rule argument

Additional information

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