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Proof step 19 from proof range-rem-in (previous step)

ri[key0] = @(m, m0, m1), ri[key] = @(m, m0, m1), key-cons(key, nodes(gstore, ginval)[@(m, m0, m1)]), @(m, m0, m1) ∈ gstore, key0 ∈ ri, key ∈ ri, key0 ∈ ri → ri[key0] ∈ gstore ∧ ¬ ri[key0].lnum ∈ ginval ∧ key-cons(key0, nodes(gstore, ginval)[ri[key0]]) ⊦ key0 = key, m ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
ri[key0] = @(m, m0, m1), ri[key] = @(m, m0, m1), key-cons(key0, nodes(gstore, ginval)[@(m, m0, m1)]), key-cons(key, nodes(gstore, ginval)[@(m, m0, m1)]), @(m, m0, m1) ∈ gstore, key0 ∈ ri, key ∈ ri ⊦ key0 = key, m ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ @(m, m0, m1).lnum = m; (s)