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Proof step 13 from proof addarray-mklist-05 (previous step)

∀ r, ty, st. addarray(r, ty, mklist(initial_value(ty), m), st) = (addarray(r, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))]) ⊦ (addarray(r, ty, mklist(initial_value(ty), m + 1) .butlast, st)[r -- n→i(m) ', mklist(initial_value(ty), m + 1) .last] [r -- _length, intval(n→i(m) + 1) ] ) = (addarray(r, initial_value(ty), n→i(m), st)[r -- n→i(m) ', initial_value(ty)][r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(m) + 1) ] )

User applied rule all left

And obtained the following new goals

Proof step 12:
addarray(r, ty, mklist(initial_value(ty), m), st) = (addarray(r, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))]) ⊦ (addarray(r, ty, mklist(initial_value(ty), m + 1) .butlast, st)[r -- n→i(m) ', mklist(initial_value(ty), m + 1) .last] [r -- _length, intval(n→i(m) + 1) ] ) = (addarray(r, initial_value(ty), n→i(m), st)[r -- n→i(m) ', initial_value(ty)][r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(m) + 1) ] )

Rule argument

[EXRARG : pos: left 1, [extquanttermlist: (r, ty, st) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, ty, st)]]