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Proof step 53 from proof eqex-tput (previous step)

∀ rk0. (rk0 ∈ st0[rk, val] -- r ↔ rk0 ∈ st1 -- r) ∧ (st0[rk, val] -- r)[rk0] = (st1 -- r)[rk0], ∀ rk. (rk ∈ st -- r ↔ rk ∈ st0 -- r) ∧ (st -- r)[rk] = (st0 -- r)[rk], eqex(st1, st0[rk, val], r), eqex(st0, st, r) ⊦ (rk0 ∈ st[rk, val] -- r ↔ rk0 ∈ st1 -- r) ∧ (st[rk, val] -- r)[rk0] = (st1 -- r)[rk0]

User applied rule structural induction

And obtained the following new goals

Proof step 52:
⊦ (∀ rk0. (rk0 ∈ st0[rk, val] -- r0 ↔ rk0 ∈ st1 -- r0) ∧ (st0[rk, val] -- r0)[rk0] = (st1 -- r0)[rk0]) ∧ (∀ rk. (rk ∈ st -- r0 ↔ rk ∈ st0 -- r0) ∧ (st -- r0)[rk] = (st0 -- r0)[rk]) ∧ eqex(st1, st0[rk, val], r0) ∧ eqex(st0, st, r0) → (r -- sk ∈ st[rk, val] -- r0 ↔ r -- sk ∈ st1 -- r0) ∧ (st[rk, val] -- r0)[r -- sk] = (st1 -- r0)[r -- sk]

Rule argument

[VARWITHFMAVARSARG : rk0, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;])]]