Application of modus ponens
mh(H)
with:
This command allows the direct use of a hypothesis of the form P ⇒ Q. If P ⇒ Q and P are hypotheses and G is the current goal, then the goal becomes Q ⇒ G. The command mh allows to use hypothesis P ⇒ Q without involving the prover, that is to say without simplifying the generated hypothesis Q. In fact, the automatic prover applies the modus ponens systematically on each P ⇒ Q and P hypothesis couple that are present in the hypothesis stack.
If P ⇒ Q or P are not hypotheses, the command isn’t applied.
The following situation has been obtained directly:
Hypothesis ENS = {e1,e2,e3,e4,e5} & zz = e5 => tt = e1 & zz = e5 Goal not(e2 = e5)
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The user wants to use the hypothesis zz = e5 => tt = e1 in order to generate the hypothesis tt = e1. He knows that hypothesis zz = e5 exists. The mh command is applied normally
PRI> mh(zz = e5 => tt = e1) Starting Modus Ponens on Hypothesis
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and the goal becomes:
Goal tt = e1 => not(e2 = e5)
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The pr or dd command allow to raise this hypothesis in the stack.