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Proof step 25 from proof nodes-write-same-flushed (previous step)

gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval)[@(m, m2, m3)] = nodes(gstore ↓, ginval)[@(m, m2, m3)], m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 27:
gstore[m] = groupblock(gndx, lax, n0), @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), m ∈ gstore, @(m, m2, m3) ∈ nodes(gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)], ginval), valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m, m2, m3)].nd = nodes(gstore ↓, ginval)[@(m, m2, m3)], m ∈ ginval

Rule argument

spec: <toplevel> name: nodes-gstore-at seq: ⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd subst: [adr, ginval, gstore] → [@(m, m2, m3), ginval, gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ]] flags: <all paths>

Additional information

Used simplifier rules: valid-group-nodes-entire: ⊦ # gndx ≤ valid-group-nodes(gndx) ↔ valid-group-nodes(gndx) = # gndx;%nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);%down-store-write-same: ⊦ @(n, n0, n1) ∈ gstore ↓[n, gblock] ↔ @(n0, n1) ∈ gblock.ladrlist;% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ @(m, m0, m1).lnum = m; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s) Used terms: @(m, m2, m3), ginval, gstore ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0) ]