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Proof step 12 from proof adr-in-index-node-key (previous step)

# gndx1 = # lax1, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), ri[key] = @(n, n0, n1), inv(groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0)), key ∈ ri, key ∈ ri → ri[key] ∈ gstore ↓ ∧ ¬ ri[key].lnum ∈ ginval ∧ key-cons(key, nodes(gstore ↓, ginval)[ri[key]]) ⊦ nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# gndx1 = # lax1, ri[key] = @(n, n0, n1), gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), inv(groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0)), key-cons(key, nodes(gstore ↓, ginval)[@(n, n0, n1)]), n ∈ gstore, key ∈ ri, @(n0, n1) ∈ prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), lax0 + @(n0, n1) ' + lax1) ⊦ n ∈ ginval, nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Rule argument

Additional information

Used simplifier rules: down-store-adr-in-explicit: ⊦ @(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ∧ @(m1, m2) ∈ gstore ↓[m0].ladrlist;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;%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).ladrlist = lax; (s)% ⊦ @(m, m0, m1).lnum = m; (s)