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Proof step 26 from proof nodes-cons-write-app (previous step)

# gndx0 = # lax0 + # lax2, # ndx = # lax0 + # lax2 + 1, # gndx1 = # lax1, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), gstore[m6] = groupblock(gndx1, lax1, m9), (gndx1 + mkgnode(nd, m1, true, boolvar0) ' + gndx0)[# lax0 + # lax1] = mkgnode(nd1, m3, boolvar, boolvar2), m6 ∈ 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) ⊦ nd1 = ndx[# lax0], dups((lax1 + lax0) + lax2), dups(lax1), dups(lax0 + lax2), dups(lax1 + lax0), dups(lax2), dups(lax0), @(m7, m8) ∈ lax2, @(m7, m8) ∈ lax0, @(m7, m8) ∈ lax1, m6 ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: group-store name: get-append-grt seq: ⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx] subst: [n, gndx0, gndx] → [# lax0 + # lax1, mkgnode(nd, m1, true, boolvar0) ' + gndx0, gndx1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: # lax0 + # lax1, mkgnode(nd, m1, true, boolvar0) ' + gndx0, gndx1