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Proof step 12 from proof referenced-adrs-lookup-keys-nodups (previous step)

nd.key = fs[adr].key, fs[referenced-adrs(ax0, ri)] = ndx + nd ' + ndx2, ri-cons(ri, fs), adr ∈ ri ⊦ dups(fs[referenced-adrs(ax0, ri)].keys), dups(ax0), adr ∈ ax0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ fs[ax] = ndx0 + ndx1 ↔ (∃ ax0, ax1. ax = ax0 + ax1 ∧ fs[ax0] = ndx0 ∧ fs[ax1] = ndx1)
Proof step 14:
nd.key = fs[adr].key, ri-cons(ri, fs), adr ∈ ri, ∃ ax2, ax1. referenced-adrs(ax0, ri) = ax2 + ax1 ∧ fs[ax2] = ndx ∧ fs[ax1] = nd ' + ndx2 ⊦ dups(ax0), dups(fs[referenced-adrs(ax0, ri)].keys), adr ∈ ax0

Rule argument

spec: aubifs-base name: read-split seq: ⊦ fs[ax] = ndx0 + ndx1 ↔ (∃ ax0, ax1. ax = ax0 + ax1 ∧ fs[ax0] = ndx0 ∧ fs[ax1] = ndx1) subst: [ndx1, ndx0, ax, fs] → [nd ' + ndx2, ndx, referenced-adrs(ax0, ri), fs] flags: <all paths>

Additional information

Used terms: nd ' + ndx2, ndx, referenced-adrs(ax0, ri), fs