48 lines
1 KiB
Text
48 lines
1 KiB
Text
import data.nat
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open nat tactic
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example (a b : nat) : a * 0 + 0 + b + 0 = b :=
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by do
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rewrite "mul_zero",
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trace_state,
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rewrite "add_zero",
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repeat $ rewrite "zero_add"
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print "---------"
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example (a b : nat) (H : a + b * 0 + 0 = b) : b = a :=
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by do
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rewrite_at "mul_zero" "H",
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trace_state,
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rewrite_at "add_zero" "H",
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rewrite_at "add_zero" "H",
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symmetry,
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assumption
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print "---------"
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example (a : nat) : (0 + a) + (0 + a) + (0 + a) = a + a + a :=
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by rewrite "zero_add"
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meta_definition rewrite_occs (th_name : name) (occs : list nat) : tactic unit :=
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do th ← mk_const th_name,
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rewrite_core reducible tt (occurrences.pos occs) ff th,
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try reflexivity
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print "---------"
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example (a : nat) : (0 + a) + (0 + a) + (0 + a) = a + a + a :=
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by do
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rewrite_occs "zero_add" [1, 3],
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trace_state,
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rewrite "zero_add"
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print "---------"
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example (a : nat) : (0 + a) + (0 + a) + (0 + a) = a + a + a :=
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by do
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rewrite_occs "zero_add" [2],
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trace_state,
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rewrite_occs "zero_add" [2],
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trace_state,
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rewrite "zero_add"
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