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Proof step 8 from proof nodes-except-refsize (previous step)

gstore1 =○refsize gstore0 ⊦ (¬ m ∈ ginval → (@(m, m0, m1) ∈ gstore1 ↔ @(m, m0, m1) ∈ gstore0)) ∧ nodes(gstore1, ginval)[@(m, m0, m1)] = nodes(gstore0, ginval)[@(m, m0, m1)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 10:
gstore1 =○refsize gstore0 ⊦ @(m, m0, m1) ∈ nodes(gstore1, ginval), (¬ m ∈ ginval → (@(m, m0, m1) ∈ gstore1 ↔ @(m, m0, m1) ∈ gstore0)) ∧ nodes(gstore1, ginval)[@(m, m0, m1)] = nodes(gstore0, ginval)[@(m, m0, m1)]
Proof step 28:
gstore1 =○refsize gstore0, @(m, m0, m1) ∈ nodes(gstore1, ginval) ⊦ (¬ m ∈ ginval → (@(m, m0, m1) ∈ gstore1 ↔ @(m, m0, m1) ∈ gstore0)) ∧ gstore1[@(m, m0, m1)].nd = nodes(gstore0, ginval)[@(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, gstore1] flags: <all paths>

Additional information

Used terms: @(m, m0, m1), ginval, gstore1