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Proof step 9 from proof val-total-01 (previous step)

pos(char, sortedchars) = pos(char2, sortedchars) ⊦ char = char2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ pos(char1, str) < # str → (pos(char1, str) = pos(char2, str) ↔ char1 = char2)
Proof step 11:
pos(char, sortedchars) = pos(char2, sortedchars) ⊦ char = char2, pos(char, sortedchars) < # sortedchars

Rule argument

spec: <toplevel> name: eqpos seq: ⊦ pos(char1, str) < # str → (pos(char1, str) = pos(char2, str) ↔ char1 = char2) subst: [char2, str, char1] → [char2, sortedchars, char] flags: <all paths>

Additional information

Used terms: char2, sortedchars, char