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Proof step 11 from proof nodes-append-subseteq (previous step)

# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), gstore[m] ↓ = groupblock(gndx0, lax0, m4), @(m1, m2) ∈ lax0, m ∈ gstore, n ∈ gstore, n0 ≤ m0 ⊦ m ∈ ginval, @(m, m1, m2) ∈ 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) ] ∧ 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) ]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ adr ∈ gstore ↔ adr.lnum ∈ gstore ∧ @(adr.pos, adr.size) ∈ gstore[adr.lnum].ladrlist
Proof step 13:
# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), gstore[m] ↓ = groupblock(gndx0, lax0, m4), n ∈ gstore, m ∈ gstore, @(m1, m2) ∈ lax0, n0 ≤ m0 ⊦ m ∈ ginval, ( @(m, m1, m2).lnum ∈ 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, m1, m2).pos, @(m, m1, m2).size) ∈ 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, m1, m2).lnum ] .ladrlist) ∧ 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) ]

Rule argument

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

Additional information

Used terms: 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, m1, m2)