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Proof step 6 from proof nodes-crash-down (previous step)

inv(gstore \ ginval) ⊦ (¬ adr.lnum ∈ ginval → (adr ∈ crash(gstore, gstore0, ginval, nx) ↓ ↔ adr ∈ gstore ↓)) ∧ ( adr ∈ crash(gstore, gstore0, ginval, nx) ↓ ∧ ¬ adr.lnum ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[adr] = nodes(gstore ↓, ginval)[adr])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
adr = @(m, m0, m1), inv(gstore \ ginval) ⊦ (¬ m ∈ ginval → (adr ∈ crash(gstore, gstore0, ginval, nx) ↓ ↔ adr ∈ gstore ↓)) ∧ ( adr ∈ crash(gstore, gstore0, ginval, nx) ↓ ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[adr] = nodes(gstore ↓, ginval)[adr])

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [adr, m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: adr, m, m0, m1