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Proof step 36 from proof nodes-append-subseteq-nodown (previous step)

# gndx = # lax, # gndx1 = # lax1, gndx0[pos(@(m1, m2), lax0)] = mkgnode(nd, m5, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m0), gstore ↓[@(m, m1, m2)] = mkgnode(nd0, m4, boolvar1, boolvar2), gstore[m] ↓ = groupblock(gndx0, lax0, m3), m ∈ gstore, n ∈ gstore, @(m1, m2) ∈ lax0 ⊦ m = n, nd = nd0, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ablock-store-inv, inst: group-store name: at seq: ⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist [pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist) ] subst: [adr, gstore] → [@(m, m1, m2), gstore ↓] flags: <all paths>

Additional information

Used simplifier rules: down-store-adr-in-explicit-simp: ⊦ gstore[m0] ↓ = groupblock(gndx, lax, n0) ∧ @(m1, m2) ∈ lax → (@(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ↓);%down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;%down-store-adr-in-explicit-simp: ⊦ gstore[m0] ↓ = groupblock(gndx, lax, n0) ∧ @(m1, m2) ∈ lax → (@(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ↓);%down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;% ⊦ @(m, m0, m1).lnum = m; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]; (s) Used terms: @(m, m1, m2), gstore ↓