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Proof step 16 from proof down-except-refsize (previous step)

(∅)[n] = groupblock(gndx0, lax0, m0), gstore1 ↓[n] = groupblock(gndx, lax, m), ∀ n. (n ∈ gstore1 ↔ n ∈ gstore0) ∧ gstore1[n].gndlist = gstore0[n].gndlist ∧ gstore1[n].ladrlist = gstore0[n].ladrlist ⊦ n ∈ gstore0, ¬ n ∈ gstore1 ∧ gndx = gndx0 ∧ lax = lax0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]
Proof step 18:
gstore1 ↓[n] = groupblock(gndx, lax, m), (∅)[n] = groupblock(gndx0, lax0, m0), n ∈ gstore1 ↓, ∀ n. (n ∈ gstore1 ↔ n ∈ gstore0) ∧ gstore1[n].gndlist = gstore0[n].gndlist ∧ gstore1[n].ladrlist = gstore0[n].ladrlist ⊦ n ∈ gstore0, ¬ n ∈ gstore1 ∧ gndx = gndx0 ∧ lax = lax0

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: notmemlookup seq: ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n] subst: [n, gstore] → [n, gstore1 ↓] flags: <all paths>

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws) Used terms: n, gstore1 ↓