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annotate Paper/src/axiom-taut.agda.replaced @ 0:14a0e409d574

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author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Sun, 24 Apr 2022 23:13:44 +0900
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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1 _!$\Rightarrow$!_ : Bool !$\rightarrow$! Bool !$\rightarrow$! Bool
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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2 false !$\Rightarrow$! _ = true
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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3 true !$\Rightarrow$! true = true
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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4 true !$\Rightarrow$! false = false
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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5
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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6 Axiom : Cond !$\rightarrow$! PrimComm !$\rightarrow$! Cond !$\rightarrow$! Set
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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7 Axiom pre comm post = !$\forall$! (env : Env) !$\rightarrow$! (pre env) !$\Rightarrow$! ( post (comm env)) !$\equiv$! true
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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8
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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9 Tautology : Cond !$\rightarrow$! Cond !$\rightarrow$! Set
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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10 Tautology pre post = !$\forall$! (env : Env) !$\rightarrow$! (pre env) !$\Rightarrow$! (post env) !$\equiv$! true