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Proof step 17 from proof nodes-append-subseteq (previous step)

# gndx = # lax, gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ] [m ] = groupblock(gndx1, lax1, m5), gstore[n] = groupblock(gndx, lax, n0), m = n, gstore[m] ↓ = groupblock(gndx0, lax0, m4), n ∈ gstore, m ∈ gstore, @(m1, m2) ∈ lax0, m ∈ gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], n0 ≤ m0 ⊦ m ∈ ginval, nodes(gstore ↓, ginval)[@(m, m1, m2)] = nodes (gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval) [@(m, m1, m2) ] ∧ @(m1, m2) ∈ lax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), n ∈ gstore, n0 ≤ m0 ⊦ n ∈ ginval, nodes(gstore ↓, ginval)[@(n, m1, m2)] = nodes (gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval) [@(n, m1, m2) ] ∧ @(m1, m2) ∈ prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr ')

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);% ⊦ n ∈ gstore[n, gblock]; (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ gstore[n, gblock][n] = gblock; (s)