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Proof step 20 from proof nodes-allocate (previous step)

gstore[m1] = groupblock(gndx0, lax0, m5), m1 ∈ gstore, @(m2, m3) ∈ lax0 ⊦ nodes(gstore[m, groupblock([], [], m0)], ginval -- m)[@(m1, m2, m3)] = nodes(gstore, ginval)[@(m1, m2, m3)], m ∈ gstore, m1 ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 22:
gstore[m1] = groupblock(gndx0, lax0, m5), @(m2, m3) ∈ lax0, m1 ∈ gstore ⊦ nodes(gstore[m, groupblock([], [], m0)], ginval -- m)[@(m1, m2, m3)] = nodes(gstore, ginval)[@(m1, m2, m3)], m1 ∈ ginval, m ∈ gstore, @(m1, m2, m3) ∈ nodes(gstore[m, groupblock([], [], m0)], ginval -- m)
Proof step 25:
gstore[m1] = groupblock(gndx0, lax0, m5), @(m2, m3) ∈ lax0, m1 ∈ gstore, @(m1, m2, m3) ∈ nodes(gstore[m, groupblock([], [], m0)], ginval -- m) ⊦ gstore[m, groupblock([], [], m0)][@(m1, m2, m3)].nd = nodes(gstore, ginval)[@(m1, m2, m3)], m1 ∈ ginval, m ∈ gstore

Rule argument

spec: <toplevel> name: nodes-gstore-at seq: ⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd subst: [adr, ginval, gstore] → [@(m1, m2, m3), ginval -- m, gstore[m, groupblock([], [], m0)]] flags: <all paths>

Additional information

Used terms: @(m1, m2, m3), ginval -- m, gstore[m, groupblock([], [], m0)]