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Proof step 24 from proof nodes-write-same-flushed (previous step)

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), m1 = m, gstore[m1] ↓ = groupblock(gndx1, lax1, m5), m ∈ gstore, m1 ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ m1 ∈ ginval, (@(m2, m3) ∈ lax0 ↔ @(m2, m3) ∈ lax1) ∧ ( @(m2, m3) ∈ lax0 → 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 25:
gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[@(m, m2, m3)] = nodes(gstore ↓, ginval)[@(m, m2, m3)], m ∈ ginval

Rule argument

Additional information

Used simplifier rules: down-block-explicit: ⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0);%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ gstore[n, gblock][n] = gblock; (s)