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

# gndx0 + # gndx1 < # lax0 + # lax1, inv(groupblock(gndx0 + gndx1, lax0 + lax1, n)) ⊦

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 + gndx1, lax0 + lax1, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (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]%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]% ⊦ m < n → ¬ n < m; (s) Used terms: groupblock(gndx0 + gndx1, lax0 + lax1, n)