## Isar proofs

proof - from some_fact have "P(x)" by simp thus ?thesis . qed

## Proof methods

Name | Parameters | Effect |
---|---|---|

assumption | — | Solves {$⟦A_1;\cdots;A_m⟧\Longrightarrow A_k$} if {$k\in[1,m]$} |

rule | a rule | Goal: {$⟦A_1;\cdots;A_m⟧\Longrightarrow C$}, rule: {$⟦P_1;\cdots P_n⟧\Longrightarrow Q$} Unifies {$C$} and {$Q$} with {$U$}, replaces the goal with: {$⟦U(A_1);\cdots;U(A_m)⟧\Longrightarrow U(P_k)$} for {$k=1,\cdots,n$} |

frule | a rule | Goal: {$⟦A_1;\cdots;A_m⟧\Longrightarrow C$}, rule: {$⟦P_1;\cdots P_n⟧\Longrightarrow Q$} Unifies {$P_1$} and {$A_j$} with {$U$} for some {$j$}, replaces the goal with: {$⟦U(A_1);\cdots;U(A_m);U(Q)⟧\Longrightarrow U(C)$} and {$⟦U(A_1);\cdots;U(A_m)⟧\Longrightarrow U(P_k)$} for {$k=2,\cdots,n$} |

drule | a rule | Same as frule, but removes {$U(A_j)$} (the {$A_j$} that was unified with {$P_1$}) |

erule | a rule | rule + drule at the same time (same unifier) |