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Proof step 3 from proof abs-log-gcrash-down (previous step)

elems nx ∩ ginval = ∅, inv(gstore \ ginval) ⊦ abs-log(nx, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx, gstore ↓)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
elems(lnum + nx1) ∩ ginval = ∅, inv(gstore \ ginval), ∀ ginval, gstore, gstore0, nx0. elems nx1 ∩ ginval = ∅ ∧ inv(gstore \ ginval) → abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx1, gstore ↓) ⊦ abs-log(lnum + nx1, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(lnum + nx1, gstore ↓)

Rule argument

indvar: nx

Additional information

Used simplifier rules: abs-log-base: ⊦ abs-log([], gstore) = [];%nat-list freely generated by [], +;;% ⊦ elems [] = ∅; (s)% ⊦ ns ∩ ∅ = ∅; (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]