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Proof step 3 from proof ls-inv-prefix-app-prefixn (previous step)

# lax1 < # gndx1, inv(groupblock(gndx0 + prefixn(# lax1, gndx1), lax0 + lax1, m)) ⊦ gndx1 = [], prefixn(# gndx0, lax0 + lax) = lax0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ablock-store-inv, inst: group-store name: inv-block seq: ⊦ inv(gblock) ↔ # gblock.gndlist = # gblock.ladrlist ∧ inv-flashsize(gblock.gndlist, gblock.ladrlist) ∧ ¬ dups(gblock.ladrlist) subst: [gblock] → [groupblock (gndx0 + prefixn(# lax1, gndx1), lax0 + lax1, m)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ m < n → m ≤ n; (s)%n ≤ # gndx ⊦ # prefixn(n, gndx) = n; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ 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% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%n ≤ # lax ⊦ prefixn(n, lax + lax0) = prefixn(n, lax); (s)%# lax ≤ m ⊦ prefixn(m, lax) = lax; (s) Used terms: groupblock(gndx0 + prefixn(# lax1, gndx1), lax0 + lax1, m)