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Proof step 22 from proof nodes-dealloc (previous step)

gstore[m] = groupblock(gndx, lax, m2), m ∈ gstore, @(m0, m1) ∈ lax ⊦ nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = nodes(gstore, ginval)[@(m, m0, m1)], m = n, @(m, m0, m1) ∈ dom nodes(gstore, ginval) | n, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 24:
gstore[m] = groupblock(gndx, lax, m2), @(m0, m1) ∈ lax, m ∈ gstore ⊦ nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = nodes(gstore, ginval)[@(m, m0, m1)], m = n, m ∈ ginval, @(m, m0, m1) ∈ dom nodes(gstore, ginval) | n, @(m, m0, m1) ∈ nodes(gstore -- n, ginval ++ n)
Proof step 27:
gstore[m] = groupblock(gndx, lax, m2), @(m0, m1) ∈ lax, m ∈ gstore, @(m, m0, m1) ∈ nodes(gstore -- n, ginval ++ n) ⊦ (gstore -- n)[@(m, m0, m1)].nd = nodes(gstore, ginval)[@(m, m0, m1)], m = n, m ∈ ginval, @(m, m0, m1) ∈ dom nodes(gstore, ginval) | n

Rule argument

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

Additional information

Used terms: @(m, m0, m1), ginval ++ n, gstore -- n