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Proof step 11 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)], @(m, m0, m1) ∈ gstore1 ∧ ¬ m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]
Proof step 13:
gstore1 =○refsize gstore0 ⊦ @(m, m0, m1) ∈ nodes(gstore1, ginval), @(m, m0, m1) ∈ gstore1 ∧ ¬ m ∈ ginval, (¬ m ∈ ginval → (@(m, m0, m1) ∈ gstore1 ↔ @(m, m0, m1) ∈ gstore0)) ∧ (∅)[@(m, m0, m1)] = nodes(gstore0, ginval)[@(m, m0, m1)]

Rule argument

spec: store, inst: node-store name: notmemlookup seq: ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr] subst: [adr, fs] → [@(m, m0, m1), nodes(gstore1, ginval)] flags: <all paths>

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);% ⊦ @(m, m0, m1).lnum = m; (s) Used terms: @(m, m0, m1), nodes(gstore1, ginval)