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Proof step 20 from proof prepost-encode-group-nodes (previous step)

# buf1 = gndx1.flashsize, # buf0 = gndx0.flashsize, # gndx0 = # lax, gndx1.flashsize < 2 * NODE_HEADER_SIZE + gndx1.head.alignedsize, abs-nodes(buf0, n, gndx0, lax, false) ⊦ # lax + # gndx1 = 0, gndx1 = []

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: list-data, inst: group-store name: elim-list-c seq: gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0 subst: [gndx, gnd, gndx0] → [gndx1, gnd, gndx]

Additional information

Used simplifier rules: ⊦ gnd + gndx = gnd ' + gndx; (s)% ⊦ (gnd ' + gndx).flashsize = gnd.flashsize + gndx.flashsize; (s)% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd ' + gndx ≠ []; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ m +1 = m + 1; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ m + n < m; (s)%gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0; (elim) Used terms: gndx1, gnd, gndx