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Proof step 15 from proof transaction-prefix-last-nonend (previous step)

# gndx0 = m1 + 1, gndx + mkgnode(nd, n, boolvar, true) ' = mkgnode(nd0, m, true, boolvar1) ' + gndx0, gndx0[m1] = mkgnode(nd1, m0, boolvar0, boolvar2), # gndx + 1 < # ndx, mkgnode(nd, n, boolvar, true) ∈ gndx0, mkgnode(nd0, m, true, boolvar1) ∈ gndx, m1 < # gndx → ¬ boolvar2, m1 < # gndx → ¬ boolvar0, ∀ n0. ¬ # gndx < n0 → (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[n0].nd = ndx[n0] ⊦ gndx0 = [], ndx = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list, inst: group-store name: lastdiv-rew seq: ⊦ gndx = [] ↔ ¬(∃ gndx0, gnd. gndx = gndx0 + gnd ') subst: [gndx] → [gndx0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ gndx + gnd ' = gndx0 + gnd0 ' ↔ gndx = gndx0 ∧ gnd = gnd0; (ws)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ # gnd ' = 0 +1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n = # gndx → (gndx + gnd ')[n] = gnd; (s)% ⊦ gnd ∈ gndx + gndx0 ↔ gnd ∈ gndx ∨ gnd ∈ gndx0; (s)% ⊦ gnd ∈ gnd0 ' ↔ gnd = gnd0; (s)%in-14: ⊦ gnd ' + gndx = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ gnd ∈ gnd0 ' + gndx ↔ gnd = gnd0 ∨ gnd ∈ gndx; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s) Used terms: gndx0