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Proof step 76 from proof prepost-gc-referenced-nodes (previous step)

# lax = # gndx0 + # gndx2 + 1, # ax2 = # gndx2, lax.to-adr(lnum) = ax1 + adr1 ' + ax2, gstore2[lnum] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax, m), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax, m)), inv(gstore2 \ ginval), ri-cons(ri, nodes(gstore2 ↓, ginval)), nd.key ∈ ri, lnum ∈ gstore2, adr1 ∈ ri ⊦ ri[nd.key] = adr1, lnum ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ lax.to-adr(n) = ax0 + ax1 ↔ (∃ lax0, lax1. lax = lax0 + lax1 ∧ ax0 = lax0.to-adr(n) ∧ ax1 = lax1.to-adr(n))
Proof step 78:
# ax2 = # gndx2, # lax = # gndx0 + # gndx2 + 1, gstore2[lnum] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax, m), inv(gstore2 \ ginval), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax, m)), ri-cons(ri, nodes(gstore2 ↓, ginval)), adr1 ∈ ri, lnum ∈ gstore2, nd.key ∈ ri, ∃ lax0, lax1. lax = lax0 + lax1 ∧ ax1 = lax0.to-adr(lnum) ∧ adr1 ' + ax2 = lax1.to-adr(lnum) ⊦ ri[nd.key] = adr1, lnum ∈ ginval

Rule argument

spec: gjournal-abs name: ladr-split seq: ⊦ lax.to-adr(n) = ax0 + ax1 ↔ (∃ lax0, lax1. lax = lax0 + lax1 ∧ ax0 = lax0.to-adr(n) ∧ ax1 = lax1.to-adr(n)) subst: [ax1, ax0, n, lax] → [adr1 ' + ax2, ax1, lnum, lax] flags: <all paths>

Additional information

Used terms: adr1 ' + ax2, ax1, lnum, lax