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Proof step 13 from proof nodes-cons-write-app (previous step)

# gndx0 = # lax0 + # lax2, # ndx = # lax0 + # lax2 + 1, # gndx = # lax, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), gstore[n] = groupblock(gndx, lax, m0), n ∈ gstore, # lax0 ≤ # gndx0, ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].end) ⊦ dups(lax + lax0), dups(lax0 + lax2), dups(lax2), dups((lax + lax0) + lax2), dups(lax), dups(lax0), @(m4, m5) ∈ lax2, @(m4, m5) ∈ lax0, @(m4, m5) ∈ lax, n ∈ ginval, ( (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ∈ gstore ∨ (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ∈ lax0.to-adr(n) ∨ (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] = @(n, m4, m5) ∨ (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ∈ lax2.to-adr(n)) ∧ gstore[n, groupblock(gndx + mkgnode(nd, m1, true, boolvar0) ' + gndx0, lax + lax0 + @(m4, m5) ' + lax2, m)] [(lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ] .nd = ndx[# lax0]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
# gndx = # lax, # ndx = # lax0 + # lax2 + 1, # gndx0 = # lax0 + # lax2, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), gstore[n] = groupblock(gndx, lax, m0), gstore[n, groupblock(gndx + mkgnode(nd, m1, true, boolvar0) ' + gndx0, lax + lax0 + @(m4, m5) ' + lax2, m)] [(lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ] = mkgnode(nd1, m3, boolvar, boolvar2), n ∈ 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] ⊦ dups(lax0), dups(lax), dups((lax + lax0) + lax2), dups(lax2), dups(lax0 + lax2), dups(lax + lax0), n ∈ ginval, @(m4, m5) ∈ lax, @(m4, m5) ∈ lax0, @(m4, m5) ∈ lax2, ( (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ∈ gstore ∨ (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ∈ lax0.to-adr(n) ∨ (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] = @(n, m4, m5) ∨ (lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ∈ lax2.to-adr(n)) ∧ nd1 = ndx[# 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] → [gstore [n, groupblock (gndx + mkgnode(nd, m1, true, boolvar0) ' + gndx0, lax + lax0 + @(m4, m5) ' + lax2, m) ] [(lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n) )[# lax0 ] ], nd1, m3, boolvar, 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: gstore [n, groupblock (gndx + mkgnode(nd, m1, true, boolvar0) ' + gndx0, lax + lax0 + @(m4, m5) ' + lax2, m) ] [(lax0.to-adr(n) + @(n, m4, m5) ' + lax2.to-adr(n))[# lax0] ], nd1, m3, boolvar, boolvar2