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Proof step 27 from proof size-0 (previous step)

(range ri | m).size = 0, ri[key] = @(m, m0, 0), gstore[m] = groupblock(gndx, lax, m1), inv(gstore \ ginval), key-cons(key, nodes(gstore ↓, ginval)[@(m, m0, 0)]), m ∈ gstore, @(m0, 0) ∈ prefixn(valid-group-nodes(gndx), lax), key ∈ ri ⊦ m ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
(range ri | m).size = 0, gstore[m] = groupblock(gndx, lax, m1), ri[key] = @(m, m0, 0), inv(gstore \ ginval), inv(groupblock(gndx, lax, m1)), key-cons(key, nodes(gstore ↓, ginval)[@(m, m0, 0)]), key ∈ ri, @(m0, 0) ∈ prefixn(valid-group-nodes(gndx), lax), m ∈ gstore ⊦ m ∈ ginval

Rule argument

Additional information

Used simplifier rules: fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base