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Proof step 12 from proof remove-refsize0-down (previous step)

gstore[n] = groupblock(gndx, lax, m), n ∈ gstore ⊦ groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m) = remove-refsize0(gstore ↓)[n], m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ablock-store-inv, inst: group-store name: at-remove-refsize0 seq: ⊦ n ∈ gstore ∧ gstore[n].ref-size ≠ 0 → remove-refsize0(gstore)[n] = gstore[n] subst: [n, gstore] → [n, gstore ↓] flags: <all paths>

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%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);%down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;%down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%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;%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)% ⊦ groupblock(gndx, lax, m).ref-size = m; (s) Used terms: n, gstore ↓