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Proof step 36 from proof nodes-transaction (previous step)

# 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
# ndx = # gndx0 + 1, # lax = # gndx, # lax2 + # lax0 = # gndx0, gstore[n] = groupblock(gndx, lax, m), (gnd ' + gndx0)[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), boolvar1, gnd = mkgnode(nd0, m0, boolvar1, boolvar2), (gnd ' + gndx0).last.end, n ∈ gstore, ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (gnd ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (gnd ' + gndx0)[n0].end), ∀ n0. ¬ # gndx0 < n0 → (gnd ' + gndx0)[n0].nd = ndx[n0] ⊦ 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

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, m0, boolvar1, boolvar2]

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, m0, boolvar1, boolvar2