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Proof step 17 from proof nodes-write-same-flushed (previous step)

gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][m1] = groupblock(gndx0, lax0, m4), gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ ( ¬ m1 ∈ ginval → ( m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ↔ @(m1, m2, m3).lnum ∈ gstore ↓ ∧ @(@(m1, m2, m3).pos, @(m1, m2, m3).size) ∈ gstore ↓[@(m1, m2, m3).lnum].ladrlist)) ∧ ( m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ∧ ¬ m1 ∈ ginval → nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[@(m1, m2, m3)] = nodes(gstore ↓, ginval)[@(m1, m2, m3)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
gstore[m] = groupblock(gndx, lax, n0), gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][m1] = groupblock(gndx0, lax0, m4), m ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ (¬ m1 ∈ ginval → m1 ∈ gstore → (@(m2, m3) ∈ lax0 ↔ @(m2, m3) ∈ gstore[m1] ↓.ladrlist)) ∧ ( m1 ∈ gstore ∧ @(m2, m3) ∈ lax0 ∧ ¬ m1 ∈ ginval → nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[@(m1, m2, m3)] = nodes(gstore ↓, ginval)[@(m1, m2, m3)])

Rule argument

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).lnum = m; (s)