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Proof step 11 from proof nodes-crash-down (previous step)

inv(gstore \ ginval) ⊦ ( ¬ m ∈ ginval → ( m ∈ crash(gstore, gstore0, ginval, nx) ∧ @(m0, m1) ∈ prefixn(valid-group-nodes(gstore[m].gndlist), gstore[m].ladrlist) ↔ @(m, m0, m1) ∈ gstore ↓)) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ crash(gstore, gstore0, ginval, nx) ↓[m].ladrlist ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[@(m, m0, m1)] = nodes(gstore ↓, ginval)[@(m, m0, m1)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
gstore[m] = groupblock(gndx, lax, m2), inv(gstore \ ginval) ⊦ (¬ m ∈ ginval → (m ∈ crash(gstore, gstore0, ginval, nx) ∧ @(m0, m1) ∈ prefixn(valid-group-nodes(gndx), lax) ↔ @(m, m0, m1) ∈ gstore ↓)) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ crash(gstore, gstore0, ginval, nx) ↓[m].ladrlist ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[@(m, m0, m1)] = nodes(gstore ↓, ginval)[@(m, m0, m1)])

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[m], gndx, lax, m2]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[m], gndx, lax, m2