Some contextual hypotheses are not included in some TCCs, making them impossible to prove.
See for example the following theory.
missing_hyp: THEORY
BEGIN
p(b: above(3))(c: nat): bool = 3 <= b + c
test
: CONJECTURE
FORALL(b:nat)
: b > 3
IMPLIES FORALL(n: (p(b))): TRUE
END missing_hyp
The only TCC generated by the type checker is shown below.
% Subtype TCC generated (at line 10, column 27) for b
% expected type above(3)
% unfinished
test_TCC1: OBLIGATION FORALL (b: nat): b > 3;
Since this TCC is related to the expression p(b) in the lemma test, the antecedent of the implication (b > 3) should be a hypothesis of the TCC as well. Such antecedent is needed to prove the TCC.
Some contextual hypotheses are not included in some TCCs, making them impossible to prove.
See for example the following theory.
The only TCC generated by the type checker is shown below.
Since this TCC is related to the expression
p(b)
in the lemmatest
, the antecedent of the implication (b > 3
) should be a hypothesis of the TCC as well. Such antecedent is needed to prove the TCC.