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Proof step 16 from proof range-rem-in (previous step)

ri[key0] = ri[key], key-cons(key, nodes(gstore, ginval)[ri[key]]), key ∈ ri, key0 ∈ ri, ri[key] ∈ gstore, ∀ key1. key1 ∈ ri → ri[key1] ∈ gstore ∧ ¬ ri[key1].lnum ∈ ginval ∧ key-cons(key1, nodes(gstore, ginval)[ri[key1]]) ⊦ key0 = key, ri[key].lnum ∈ ginval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
ri[key0] = ri[key], ri[key] = @(m, m0, m1), key-cons(key, nodes(gstore, ginval)[ri[key]]), ri[key] ∈ gstore, key0 ∈ ri, key ∈ ri, ∀ key1. key1 ∈ ri → ri[key1] ∈ gstore ∧ ¬ ri[key1].lnum ∈ ginval ∧ key-cons(key1, nodes(gstore, ginval)[ri[key1]]) ⊦ key0 = key, m ∈ ginval

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [ri[key], m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: ri[key], m, m0, m1