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Proof step 28 from proof nodes-cons-write-app (previous step)

# gndx1 = # lax1, # ndx = # lax0 + # lax2 + 1, # gndx0 = # lax0 + # lax2, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[# lax0 + # lax1 - # gndx1] = mkgnode(nd1, m3, boolvar, boolvar2), gstore[m6] = groupblock(gndx1, lax1, m9), m6 ∈ gstore, # lax0 ≤ # gndx0, ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].end), ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].nd = ndx[n0] ⊦ nd1 = ndx[# lax0], # lax0 + # lax1 < # gndx1, dups(lax0), dups(lax2), dups(lax1 + lax0), dups(lax0 + lax2), dups(lax1), dups((lax1 + lax0) + lax2), m6 ∈ ginval, @(m7, m8) ∈ lax1, @(m7, m8) ∈ lax0, @(m7, m8) ∈ lax2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# gndx1 = # lax1, # ndx = # lax0 + # lax2 + 1, # gndx0 = # lax0 + # lax2, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), gstore[m6] = groupblock(gndx1, lax1, m9), (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[# lax0] = mkgnode(nd1, m3, boolvar, boolvar2), m6 ∈ gstore, # lax0 ≤ # gndx0, ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].end), ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].nd = ndx[n0] ⊦ nd1 = ndx[# lax0], dups(lax0), dups(lax2), dups(lax1 + lax0), dups(lax0 + lax2), dups(lax1), dups((lax1 + lax0) + lax2), m6 ∈ ginval, @(m7, m8) ∈ lax1, @(m7, m8) ∈ lax0, @(m7, m8) ∈ lax2

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n - m = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)