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Proof step 12 from proof nodes-ginval-inter (previous step)

gstore[m] = groupblock(gndx, lax, m2), dom gstore ∩ ginval = ∅, @(m0, m1) ∈ lax, m ∈ gstore ⊦ nodes(gstore, ginval)[@(m, m0, m1)] = nodes(gstore, ∅)[@(m, m0, m1)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 14:
gstore[m] = groupblock(gndx, lax, m2), dom gstore ∩ ginval = ∅, m ∈ gstore, @(m0, m1) ∈ lax, @(m, m0, m1) ∈ nodes(gstore, ginval) ⊦ gstore[@(m, m0, m1)].nd = nodes(gstore, ∅)[@(m, m0, m1)]

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, gstore] flags: <all paths>

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);% ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)%⊦ gstore[n] = groupblock(gndx, lax, m0) ∧ n ∈ gstore ∧ @(n0, n1) ∈ lax → @(n, n0, n1) ∈ gstore; (ss)% ⊦ @(m, m0, m1).lnum = m; (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]% ⊦ ns ∩ dom gstore = ∅ ∧ n ∈ gstore → ¬ n ∈ ns; (s) Used terms: @(m, m0, m1), ginval, gstore