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Proof step 36 from proof nodes-write-same-flushed (previous step)

gstore ↓[@(m, m2, m3)] = mkgnode(nd0, m4, boolvar1, boolvar2), gstore[m] = groupblock(gndx, lax, n0), prefixn(valid-group-nodes(gndx), gndx)[pos(@(m2, m3), lax)] = mkgnode(nd, m1, boolvar, boolvar0), m ∈ gstore, @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ nd = nd0, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ablock-store-inv, inst: group-store name: at seq: ⊦ adr ∈ gstore → gstore[adr] = gstore[adr.lnum].gndlist [pos(@(adr.pos, adr.size), gstore[adr.lnum].ladrlist) ] subst: [adr, gstore] → [@(m, m2, m3), gstore ↓] flags: <all paths>

Additional information

Used simplifier rules: 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);%valid-group-nodes-entire: ⊦ # gndx ≤ valid-group-nodes(gndx) ↔ valid-group-nodes(gndx) = # gndx;%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;%down-store-adr-in-explicit: ⊦ @(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ∧ @(m1, m2) ∈ gstore ↓[m0].ladrlist;%down-block-explicit: ⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0);%valid-group-nodes-entire: ⊦ # gndx ≤ valid-group-nodes(gndx) ↔ valid-group-nodes(gndx) = # gndx;% ⊦ @(m, m0, m1).lnum = m; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)%⊦ ladr ∈ prefixn(n, lax) → pos(ladr, prefixn(n, lax)) = pos(ladr, lax); (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s) Used terms: @(m, m2, m3), gstore ↓