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Proof step 21 from proof nodes-crash-down (previous step)

gstore[m] = groupblock(gndx, lax, m2), (m ∈ nx ∨ ¬ m ∈ ginval ⊃ groupblock(gndx, lax, (m ∈ gstore0 ⊃ gstore0[m].ref-size;0));gstore0[m]) ↓ = groupblock(gndx0, lax0, m3), inv(gstore \ ginval), m ∈ crash(gstore, gstore0, ginval, nx) ⊦ @(m, m0, m1) ∈ nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval), (¬ m ∈ ginval → (m ∈ gstore ∧ @(m0, m1) ∈ prefixn(valid-group-nodes(gndx), lax) ↔ @(m, m0, m1) ∈ gstore ↓)) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax0 ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[@(m, m0, m1)] = nodes(gstore ↓, ginval)[@(m, m0, m1)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
gstore[m] = groupblock(gndx, lax, m2), (m ∈ nx ∨ ¬ m ∈ ginval ⊃ groupblock(gndx, lax, (m ∈ gstore0 ⊃ gstore0[m].ref-size;0));gstore0[m]) ↓ = groupblock(gndx0, lax0, m3), inv(gstore \ ginval), m ∈ crash(gstore, gstore0, ginval, nx) ⊦ (¬ m ∈ ginval → (m ∈ gstore ∧ @(m0, m1) ∈ prefixn(valid-group-nodes(gndx), lax) ↔ @(m, m0, m1) ∈ gstore ↓)) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax0 ∧ ¬ m ∈ ginval → nodes(crash(gstore, gstore0, ginval, nx) ↓, ginval)[@(m, m0, m1)] = nodes(gstore ↓, ginval)[@(m, m0, m1)]), @(m0, m1) ∈ prefixn(valid-group-nodes(gndx), lax) ∧ ¬ m ∈ ginval

Rule argument

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);%down-store-adr-in-explicit: ⊦ @(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ∧ @(m1, m2) ∈ gstore ↓[m0].ladrlist;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;%down-block-explicit: ⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0);% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ @(m, m0, m1).lnum = m; (s)%⊦ n ∈ crash(gstore, gstore0, ginval, nx) → crash(gstore, gstore0, ginval, nx)[n] = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock (gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)) ;gstore0[n] ); (s)