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Proof step 33 from proof nodes-transaction (previous step)

# lax = # gndx, # ndx = # gndx1, # lax2 + # lax0 + 1 = # gndx1, gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), n ∈ gstore, ∀ n. n < # gndx1 → gndx1[n].nd = ndx[n], gndx1 = [] ∨ gndx1.head.start ∧ gndx1.last.end ∧ (∀ n. (0 < n ∧ n < # gndx1 → ¬ gndx1[n].start) ∧ (n + 1 < # gndx1 → ¬ gndx1[n].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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
# lax = # gndx, # ndx = # gndx1, # lax2 + # lax0 + 1 = # gndx1, gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), gndx1.last.end, gndx1.head.start, n ∈ gstore, ∀ n. n < # gndx1 → gndx1[n].nd = ndx[n], ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx1 → ¬ gndx1[n0].start) ∧ (n0 + 1 < # gndx1 → ¬ gndx1[n0].end) ⊦ gndx1 = [], 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: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # [] = 0; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)