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Proof step 33 from proof down-except-refsize (previous step)

gstore0[n] = groupblock(gndx0, lax0, m0), n ∈ gstore0, n ∈ gstore1, ∀ n. (n ∈ gstore1 ↔ n ∈ gstore0) ∧ gstore1[n].gndlist = gstore0[n].gndlist ∧ gstore1[n].ladrlist = gstore0[n].ladrlist ⊦ prefixn(valid-group-nodes(gstore1[n].gndlist), gstore1[n].gndlist) = prefixn(valid-group-nodes(gndx0), gndx0) ∧ prefixn(valid-group-nodes(gstore1[n].gndlist), gstore1[n].ladrlist) = prefixn(valid-group-nodes(gndx0), lax0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
gstore0[n] = groupblock(gndx0, lax0, m0), gstore1[n] = groupblock(gndx, lax, m), n ∈ gstore1, n ∈ gstore0, ∀ n. (n ∈ gstore1 ↔ n ∈ gstore0) ∧ gstore1[n].gndlist = gstore0[n].gndlist ∧ gstore1[n].ladrlist = gstore0[n].ladrlist ⊦ prefixn(valid-group-nodes(gndx), gndx) = prefixn(valid-group-nodes(gndx0), gndx0) ∧ prefixn(valid-group-nodes(gndx), lax) = prefixn(valid-group-nodes(gndx0), lax0)

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] → [gstore1[n], gndx, lax, m]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore1[n], gndx, lax, m