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Proof step 46 from proof prepost-gc-referenced-nodes (previous step)

# lax = # gndx2, # gndx0 = # lax1, gstore2[m1] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m), ri[nd.key] = @(m1, m2, m3), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m)), inv(gstore2 \ ginval), ri-cons(ri, nodes(gstore2 ↓, ginval)), m1 ∈ gstore2, nd.key ∈ ri ⊦ nd = nodes(gstore2 ↓, ginval)[@(m1, m2, m3)], m1 ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 48:
# gndx0 = # lax1, # lax = # gndx2, ri[nd.key] = @(m1, m2, m3), gstore2[m1] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m), inv(gstore2 \ ginval), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m)), ri-cons(ri, nodes(gstore2 ↓, ginval)), nd.key ∈ ri, m1 ∈ gstore2, @(m1, m2, m3) ∈ nodes(gstore2 ↓, ginval) ⊦ nd = gstore2 ↓[@(m1, m2, m3)].nd, m1 ∈ ginval

Rule argument

spec: gjournal-abs name: nodes-gstore-at seq: ⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd subst: [adr, ginval, gstore] → [@(m1, m2, m3), ginval, gstore2 ↓] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ key ∈ ri ∧ ri[key] = adr ∧ ri-cons(ri, fs) → adr ∈ fs; (ss) Used terms: @(m1, m2, m3), ginval, gstore2 ↓