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Proof step 18 from proof range-rem-in (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 19:
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

Rule argument

pos: left 7 terms: key0 abort: F discard: T computed: T

Additional information

Used terms: key0